Method and apparatus for improved implicit transform selection

ABSTRACT

In a method of video encoding for an encoder, a determination is made to determine whether (i) an implicit transform scheme is enabled, and (ii) at least one of a low-frequency non-separable transform (LFNST) and a matrix-based intra predication mode (MIP) is invalid for a coding unit (CU). In response to the determination that the implicit transform scheme is enabled, and at least one of the LFNST and MIP is invalid, a primary transform type is determined based on a size of the CU. A primary transform is performed for a transform block that is partitioned from the CU in accordance with the determined primary transform type. A coded bitstream that indicates the primary transform type of the CU is subsequently output.

INCORPORATION BY REFERENCE

This application is a continuation of U.S. patent application Ser. No.16/883,545, “METHOD AND APPARATUS FOR IMPROVED IMPLICIT TRANSFORMSELECTION” filed on May 26, 2020, which claims the benefit of priorityto U.S. Provisional Application No. 62/858,887, “IMPROVED IMPLICITTRANSFORM SELECTION” filed on Jun. 7, 2019. The entire disclosures ofthe above-identified applications are incorporated herein by referencein their entirety.

TECHNICAL FIELD

The present disclosure presents a set of advanced video codingtechnologies. More specifically, a modified implicit tran33sformapproach is proposed.

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent the work is described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

Video coding and decoding can be performed using inter-pictureprediction with motion compensation. Uncompressed digital video caninclude a series of pictures, each picture having a spatial dimensionof, for example, 1920×1080 luminance samples and associated chrominancesamples. The series of pictures can have a fixed or variable picturerate (informally also known as frame rate), of, for example 60 picturesper second or 60 Hz. Uncompressed video has significant bitraterequirements. For example, 1080p60 4:2:0 video at 8 bit per sample(1920×1080 luminance sample resolution at 60 Hz frame rate) requiresclose to 1.5 Gbit/s bandwidth. An hour of such video requires more than600 gigabytes (GB) of storage space.

One purpose of video coding and decoding can be the reduction ofredundancy in the input video signal, through compression. Compressioncan help reduce the aforementioned bandwidth or storage spacerequirements, in some cases by two orders of magnitude or more. Bothlossless and lossy compression, as well as a combination thereof can beemployed. Lossless compression refers to techniques where an exact copyof the original signal can be reconstructed from the compressed originalsignal. When using lossy compression, the reconstructed signal may notbe identical to the original signal, but the distortion between originaland reconstructed signals is small enough to make the reconstructedsignal useful for the intended application. In the case of video, lossycompression is widely employed. The amount of distortion tolerateddepends on the application; for example, users of certain consumerstreaming applications may tolerate higher distortion than users oftelevision distribution applications. The compression ratio achievablecan reflect that: higher allowable/tolerable distortion can yield highercompression ratios.

A video encoder and decoder can utilize techniques from several broadcategories, including, for example, motion compensation, transform,quantization, and entropy coding.

Video codec technologies can include techniques known as intra coding.In intra coding, sample values are represented without reference tosamples or other data from previously reconstructed reference pictures.In some video codecs, the picture is spatially subdivided into blocks ofsamples. When all blocks of samples are coded in intra mode, thatpicture can be an intra picture. Intra pictures and their derivationssuch as independent decoder refresh pictures, can be used to reset thedecoder state and can, therefore, be used as the first picture in acoded video bitstream and a video session, or as a still image. Thesamples of an intra block can be exposed to a transform, and thetransform coefficients can be quantized before entropy coding. Intraprediction can be a technique that minimizes sample values in thepre-transform domain. In some cases, the smaller the DC value after atransform is, and the smaller the AC coefficients are, the fewer thebits that are required at a given quantization step size to representthe block after entropy coding.

Traditional intra coding such as known from, for example MPEG-2generation coding technologies, does not use intra prediction. However,some newer video compression technologies include techniques thatattempt, from, for example, surrounding sample data and/or metadataobtained during the encoding/decoding of spatially neighboring, andpreceding in decoding order, blocks of data. Such techniques arehenceforth called “intra prediction” techniques. Note that in at leastsome cases, intra prediction is only using reference data from thecurrent picture under reconstruction and not from reference pictures.

There can be many different forms of intra prediction. When more thanone of such techniques can be used in a given video coding technology,the technique in use can be coded in an intra prediction mode. Incertain cases, modes can have submodes and/or parameters, and those canbe coded individually or included in the mode codeword. Which codewordto use for a given mode/submode/parameter combination can have an impactin the coding efficiency gain through intra prediction, and so can theentropy coding technology used to translate the codewords into abitstream.

A certain mode of intra prediction was introduced with H.264, refined inH.265, and further refined in newer coding technologies such as jointexploration model (JEM), versatile video coding (VVC), and benchmark set(BMS). A predictor block can be formed using neighboring sample valuesbelonging to already available samples. Sample values of neighboringsamples are copied into the predictor block according to a direction. Areference to the direction in use can be coded in the bitstream or mayitself be predicted.

SUMMARY

Aspects of the disclosure provide methods and apparatuses for videoencoding/decoding. In some examples, an apparatus for video decodingincludes receiving circuitry and processing circuitry.

According to an aspect of the disclosure, a method of video decoding fora decoder is provided. In the method, transform block signalinginformation is acquired from a coded video bitstream. In addition, adetermination is made to determine whether the transform block signalinginformation indicates an implicit transform scheme, and at least one ofa low-frequency non-separable transform (LFNST) and a matrix-based intrapredication mode (MIP) is invalid. In response to the determination thatthe transform block signaling information indicates the implicittransform scheme, and at least one of the LFNST and MIP is signaled asinvalid, a primary transform type is determined based on a size of acoding block unit (CU), and a primary transform is performed for atransform block that is partitioned from the CU in accordance with thedetermined primary transform type.

In some embodiments, in order to determine the primary transform type, adetermination can be made to determine whether a transform skip mode isenabled. In response to the determination that the transform skip modeis not enabled, a transform type DST-7 can be determined for ahorizontal transform for the transform block, responsive to a width ofthe CU being equal to or greater than T1 and equal to or less than T2. Atransform type DCT-2 can be determined for the horizontal transform forthe transform block, responsive to the width of the CU being less thanT1 or greater than T2. A transform type DST-7 can be determined for avertical transform for the transform block responsive to a height of theCU being equal to or greater than T1 and equal to or less than T2. Atransform type DCT-2 can be determined for the vertical transform forthe transform block responsive to the height of the CU being less thanT1 or greater than T2.

In some embodiments, the T1 can be equal to 2 pixels, 4 pixels, or 8pixels, and T2 is equal to one of 4 pixels, 8 pixels, 16 pixels, or 32pixels.

In response to the determination that that the transform block signalinginformation indicates the implicit transform scheme, and the at leastone of the LFNST or MIP is signaled as true, in a first example, a firsttransform type DCT-2 can be determined for the transform block. In asecond example, a second transform type that is not DCT-7 can bedetermined for the transform block, where the second transform typeincludes at least one of DST-1, DCT-5, compound orthonormal transform(COT), or karhunen-loève transform.

in response to the determination that that the transform block signalinginformation indicates the implicit transform scheme, and the MIP issignaled as false which indicates the MIP is not applied for thetransform block, a transform type DST-7 can be determined for ahorizontal transform for the transform block responsive to a width ofthe CU being equal to or greater than T1 and equal to or less than T2. Atransform type DCT-2 can be determined for the horizontal transform forthe transform block responsive to the width of the CU being less than T1or greater than T2. A transform type DST-7 can be determined for avertical transform for the transform block responsive to a height of theCU being equal to or greater than T1 and equal to or less than T2. Atransform type DCT-2 can be determined for the vertical transform forthe transform block responsive to the height of the CU being less thanT1 or greater than T2.

In a first example, T1 can be equal to 2 pixels, and T2 can be equal toone of 4 pixels or 8 pixels. In a second example, T1 can be equal to 4pixels, and T2 can be equal to one of 4 pixels or 8 pixels. In a thirdexample, T1 can be equal to 8 pixels, and T2 can be equal to one of 8pixels, 16 pixels, or 32 pixels. In a fourth example, T1 can be equal to16 pixels, and T2 can be equal to one of 16 pixels or 32 pixels.

In some embodiments, in response to the determination that that thetransform block signaling information indicates the implicit transformscheme, and both the LFNST and the MIP are signaled as false whichindicates neither the LFNST or the MIP is applied for the transformblock, a transform type DST-7 can be determined for a horizontaltransform for the transform block responsive to a width of the CU beingequal to or greater than T1 and equal to or less than T2. A transformtype DCT-2 can be determined for the horizontal transform for thetransform block responsive to the width of the CU being less than T1 orgreater than T2. A transform type DST-7 can be determined for a verticaltransform for the transform block responsive to a height of the CU beingequal to or greater than T1 and equal to or less than T2. A transformtype DCT-2 can be determined for the vertical transform of the transformblock responsive to the height of the CU being less than T1 or greaterthan T2.

According to another aspect of the disclosure, a method of videodecoding for a decoder is provided. In the method, a transform blocksignaling information is acquired from the coded video bitstream. Aprimary transform type is determined based on the transformation blocksignaling information and a size of the coding block unit (CU). Aprimary transform is performed for the transform block that ispartitioned from the CU in accordance with the determined primarytransform type.

In some embodiments, in order to determine the primary transform type, atransform type DST-7 can be determined for a horizontal transform forthe transform block responsive to a width of the CU being equal to orgreater than T1 and equal to or less than T2. A transform type based ona signaled index from the transformation block signaling information canbe determined for the horizontal transform of the transform block,responsive to the width of the CU being greater than T2 and equal to orless than T3. The signaled index indicates that the transform type isone of DCT-2 or DST-7. A transform type DCT-2 can be determined for thehorizontal transform for the transform block responsive to the width ofthe CU being less than T1 or greater than T3.

In some embodiments, in order to determine the primary transform type, atransform type DST-7 can be determined for a vertical transform for thetransform block responsive to a height of the CU being equal to orgreater than T1 and equal to or less than T2. A transform type based ona signaled index from the transformation block signaling information canbe determined for the vertical transform for the transform block,responsive to the height of the CU being greater than T2 and equal to orless than T3. The signaled index indicates that the transform type isone of DCT-2 or DST-7. A transform type DCT-2 can be determined for thevertical transform for the transform block responsive to the height ofthe CU being less than T1 or greater than T3.

In some embodiments, the T1 can be equal to one of 2 pixels, 4 pixels,or 8 pixels. The T2 can be equal to one of 4 pixels, 8 pixels, 16pixels, or 32 pixels, and the T3 can be equal to one of 8 pixels, 16pixels, 32 pixels, or 64 pixels.

Aspects of the disclosure also provide a non-transitorycomputer-readable medium storing instructions which when executed by acomputer for video decoding cause the computer to perform the method forvideo decoding.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features, the nature, and various advantages of the disclosedsubject matter will be more apparent from the following detaileddescription and the accompanying drawings in which:

FIG. 1 is a schematic illustration of a simplified block diagram of acommunication system (100) in accordance with an embodiment.

FIG. 2 is a schematic illustration of a simplified block diagram of acommunication system (200) in accordance with an embodiment.

FIG. 3 is a schematic illustration of a simplified block diagram of adecoder in accordance with an embodiment.

FIG. 4 is a schematic illustration of a simplified block diagram of anencoder in accordance with an embodiment.

FIG. 5 shows a block diagram of an encoder in accordance with anotherembodiment.

FIG. 6 shows a block diagram of a decoder in accordance with anotherembodiment.

FIGS. 7A-7D show four exemplary sub-block transform modes.

FIG. 8 shows a first exemplary division of a luma intra-predicted blockbased on Intra Sub-Partitions (ISP) coding mode.

FIG. 9 shows a second exemplary division of luma intra-predicted blockbased on Intra Sub-Partitions (ISP) coding mode.

FIG. 10 shows a reduced secondary transform (RST) using a 16×64secondary transform core.

FIG. 11 shows a reduced secondary transform (RST) using a 16×48secondary transform core.

FIG. 12A shows a forward reduced transform.

FIG. 12B shows an inverse reduced transform.

FIG. 13A shows a first embodiment of RST8×8.

FIG. 13B shows a second embodiment of RST8×8.

FIG. 14 shows a Matrix-based intra prediction (MIP) mode.

FIG. 15 shows a flow chart outlining a process example according to someembodiments of the disclosure.

FIG. 16 is a schematic illustration of a computer system in accordancewith an embodiment.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 1 illustrates a simplified block diagram of a communication system(100) according to an embodiment of the present disclosure. Thecommunication system (100) includes a plurality of terminal devices thatcan communicate with each other, via, for example, a network (150). Forexample, the communication system (100) includes a first pair ofterminal devices (110) and (120) interconnected via the network (150).In the FIG. 1 example, the first pair of terminal devices (110) and(120) performs unidirectional transmission of data. For example, theterminal device (110) may code video data (e.g., a stream of videopictures that are captured by the terminal device (110)) fortransmission to the other terminal device (120) via the network (150).The encoded video data can be transmitted in the form of one or morecoded video bitstreams. The terminal device (120) may receive the codedvideo data from the network (150), decode the coded video data torecover the video pictures and display video pictures according to therecovered video data. Unidirectional data transmission may be common inmedia serving applications and the like.

In another example, the communication system (100) includes a secondpair of terminal devices (130) and (140) that performs bidirectionaltransmission of coded video data that may occur, for example, duringvideoconferencing. For bidirectional transmission of data, in anexample, each terminal device of the terminal devices (130) and (140)may code video data (e.g., a stream of video pictures that are capturedby the terminal device) for transmission to the other terminal device ofthe terminal devices (130) and (140) via the network (150). Eachterminal device of the terminal devices (130) and (140) also may receivethe coded video data transmitted by the other terminal device of theterminal devices (130) and (140), and may decode the coded video data torecover the video pictures and may display video pictures at anaccessible display device according to the recovered video data.

In the FIG. 1 example, the terminal devices (110), (120), (130) and(140) may be illustrated as servers, personal computers and smart phonesbut the principles of the present disclosure may be not so limited.Embodiments of the present disclosure find application with laptopcomputers, tablet computers, media players and/or dedicated videoconferencing equipment. The network (150) represents any number ofnetworks that convey coded video data among the terminal devices (110),(120), (130) and (140), including for example wireline (wired) and/orwireless communication networks. The communication network (150) mayexchange data in circuit-switched and/or packet-switched channels.Representative networks include telecommunications networks, local areanetworks, wide area networks and/or the Internet. For the purposes ofthe present discussion, the architecture and topology of the network(150) may be immaterial to the operation of the present disclosureunless explained herein below.

FIG. 2 illustrates, as an example for an application for the disclosedsubject matter, the placement of a video encoder and a video decoder ina streaming environment. The disclosed subject matter can be equallyapplicable to other video enabled applications, including, for example,video conferencing, digital TV, storing of compressed video on digitalmedia including CD, DVD, memory stick and the like, and so on.

A streaming system may include a capture subsystem (213), that caninclude a video source (201), for example a digital camera, creating forexample a stream of video pictures (202) that are uncompressed. In anexample, the stream of video pictures (202) includes samples that aretaken by the digital camera. The stream of video pictures (202),depicted as a bold line to emphasize a high data volume when compared toencoded video data (204) (or coded video bitstreams), can be processedby an electronic device (220) that includes a video encoder (203)coupled to the video source (201). The video encoder (203) can includehardware, software, or a combination thereof to enable or implementaspects of the disclosed subject matter as described in more detailbelow. The encoded video data (204) (or encoded video bitstream (204)),depicted as a thin line to emphasize the lower data volume when comparedto the stream of video pictures (202), can be stored on a streamingserver (205) for future use. One or more streaming client subsystems,such as client subsystems (206) and (208) in FIG. 2 can access thestreaming server (205) to retrieve copies (207) and (209) of the encodedvideo data (204). A client subsystem (206) can include a video decoder(210), for example, in an electronic device (230). The video decoder(210) decodes the incoming copy (207) of the encoded video data andcreates an outgoing stream of video pictures (211) that can be renderedon a display (212) (e.g., display screen) or other rendering device (notdepicted). In some streaming systems, the encoded video data (204),(207), and (209) (e.g., video bitstreams) can be encoded according tocertain video coding/compression standards. Examples of those standardsinclude ITU-T Recommendation H.265. In an example, a video codingstandard under development is informally known as Versatile Video Coding(VVC). The disclosed subject matter may be used in the context of VVC.

It is noted that the electronic devices (220) and (230) can includeother components (not shown). For example, the electronic device (220)can include a video decoder (not shown) and the electronic device (230)can include a video encoder (not shown) as well.

FIG. 3 shows a block diagram of a video decoder (310) according to anembodiment of the present disclosure. The video decoder (310) can beincluded in an electronic device (330). The electronic device (330) caninclude a receiver (331) (e.g., receiving circuitry). The video decoder(310) can be used in the place of the video decoder (210) in the FIG. 2example.

The receiver (331) may receive one or more coded video sequences to bedecoded by the video decoder (310); in the same or another embodiment,one coded video sequence at a time, where the decoding of each codedvideo sequence is independent from other coded video sequences. Thecoded video sequence may be received from a channel (301), which may bea hardware/software link to a storage device which stores the encodedvideo data. The receiver (331) may receive the encoded video data withother data, for example, coded audio data and/or ancillary data streams,that may be forwarded to their respective using entities (not depicted).The receiver (331) may separate the coded video sequence from the otherdata. To combat network jitter, a buffer memory (315) may be coupled inbetween the receiver (331) and an entropy decoder/parser (320) (“parser(320)” henceforth). In certain applications, the buffer memory (315) ispart of the video decoder (310). In others, it can be outside of thevideo decoder (310) (not depicted). In still others, there can be abuffer memory (not depicted) outside of the video decoder (310), forexample to combat network jitter, and in addition another buffer memory(315) inside the video decoder (310), for example to handle playouttiming. When the receiver (331) is receiving data from a store/forwarddevice of sufficient bandwidth and controllability, or from anisosynchronous network, the buffer memory (315) may not be needed, orcan be small. For use on best effort packet networks such as theInternet, the buffer memory (315) may be required, can be comparativelylarge and can be advantageously of adaptive size, and may at leastpartially be implemented in an operating system or similar elements (notdepicted) outside of the video decoder (310).

The video decoder (310) may include the parser (320) to reconstructsymbols (321) from the coded video sequence. Categories of those symbolsinclude information used to manage operation of the video decoder (310),and potentially information to control a rendering device such as arender device (312) (e.g., a display screen) that is not an integralpart of the electronic device (330) but can be coupled to the electronicdevice (330), as was shown in FIG. 3 . The control information for therendering device(s) may be in the form of Supplemental EnhancementInformation (SEI messages) or Video Usability Information (VUI)parameter set fragments (not depicted). The parser (320) mayparse/entropy-decode the coded video sequence that is received. Thecoding of the coded video sequence can be in accordance with a videocoding technology or standard, and can follow various principles,including variable length coding, Huffman coding, arithmetic coding withor without context sensitivity, and so forth. The parser (320) mayextract from the coded video sequence, a set of subgroup parameters forat least one of the subgroups of pixels in the video decoder, based uponat least one parameter corresponding to the group. Subgroups can includeGroups of Pictures (GOPs), pictures, tiles, slices, macroblocks, CodingUnits (CUs), blocks, Transform Units (TUs), Prediction Units (PUs) andso forth. The parser (320) may also extract from the coded videosequence information such as transform coefficients, quantizer parametervalues, motion vectors, and so forth.

The parser (320) may perform an entropy decoding/parsing operation onthe video sequence received from the buffer memory (315), so as tocreate symbols (321).

Reconstruction of the symbols (321) can involve multiple different unitsdepending on the type of the coded video picture or parts thereof (suchas: inter and intra picture, inter and intra block), and other factors.Which units are involved, and how, can be controlled by the subgroupcontrol information that was parsed from the coded video sequence by theparser (320). The flow of such subgroup control information between theparser (320) and the multiple units below is not depicted for clarity.

Beyond the functional blocks already mentioned, the video decoder (310)can be conceptually subdivided into a number of functional units asdescribed below. In a practical implementation operating undercommercial constraints, many of these units interact closely with eachother and can, at least partly, be integrated into each other. However,for the purpose of describing the disclosed subject matter, theconceptual subdivision into the functional units below is appropriate.

A first unit is the scaler/inverse transform unit (351). Thescaler/inverse transform unit (351) receives a quantized transformcoefficient as well as control information, including which transform touse, block size, quantization factor, quantization scaling matrices,etc. as symbol(s) (321) from the parser (320). The scaler/inversetransform unit (351) can output blocks comprising sample values, thatcan be input into aggregator (355).

In some cases, the output samples of the scaler/inverse transform (351)can pertain to an intra coded block; that is: a block that is not usingpredictive information from previously reconstructed pictures, but canuse predictive information from previously reconstructed parts of thecurrent picture. Such predictive information can be provided by an intrapicture prediction unit (352). In some cases, the intra pictureprediction unit (352) generates a block of the same size and shape ofthe block under reconstruction, using surrounding already reconstructedinformation fetched from the current picture buffer (358). The currentpicture buffer (358) buffers, for example, partly reconstructed currentpicture and/or fully reconstructed current picture. The aggregator(355), in some cases, adds, on a per sample basis, the predictioninformation the intra prediction unit (352) has generated to the outputsample information as provided by the scaler/inverse transform unit(351).

In other cases, the output samples of the scaler/inverse transform unit(351) can pertain to an inter coded, and potentially motion compensatedblock. In such a case, a motion compensation prediction unit (353) canaccess reference picture memory (357) to fetch samples used forprediction. After motion compensating the fetched samples in accordancewith the symbols (321) pertaining to the block, these samples can beadded by the aggregator (355) to the output of the scaler/inversetransform unit (351) (in this case called the residual samples orresidual signal) so as to generate output sample information. Theaddresses within the reference picture memory (357) from where themotion compensation prediction unit (353) fetches prediction samples canbe controlled by motion vectors, available to the motion compensationprediction unit (353) in the form of symbols (321) that can have, forexample X, Y, and reference picture components. Motion compensation alsocan include interpolation of sample values as fetched from the referencepicture memory (357) when sub-sample exact motion vectors are in use,motion vector prediction mechanisms, and so forth.

The output samples of the aggregator (355) can be subject to variousloop filtering techniques in the loop filter unit (356). Videocompression technologies can include in-loop filter technologies thatare controlled by parameters included in the coded video sequence (alsoreferred to as coded video bitstream) and made available to the loopfilter unit (356) as symbols (321) from the parser (320), but can alsobe responsive to meta-information obtained during the decoding ofprevious (in decoding order) parts of the coded picture or coded videosequence, as well as responsive to previously reconstructed andloop-filtered sample values.

The output of the loop filter unit (356) can be a sample stream that canbe output to the render device (312) as well as stored in the referencepicture memory (357) for use in future inter-picture prediction.

Certain coded pictures, once fully reconstructed, can be used asreference pictures for future prediction. For example, once a codedpicture corresponding to a current picture is fully reconstructed andthe coded picture has been identified as a reference picture (by, forexample, the parser (320)), the current picture buffer (358) can becomea part of the reference picture memory (357), and a fresh currentpicture buffer can be reallocated before commencing the reconstructionof the following coded picture.

The video decoder (310) may perform decoding operations according to apredetermined video compression technology in a standard, such as ITU-TRec. H.265. The coded video sequence may conform to a syntax specifiedby the video compression technology or standard being used, in the sensethat the coded video sequence adheres to both the syntax of the videocompression technology or standard and the profiles as documented in thevideo compression technology or standard. Specifically, a profile canselect certain tools as the only tools available for use under thatprofile from all the tools available in the video compression technologyor standard. Also necessary for compliance can be that the complexity ofthe coded video sequence is within bounds as defined by the level of thevideo compression technology or standard. In some cases, levels restrictthe maximum picture size, maximum frame rate, maximum reconstructionsample rate (measured in, for example megasamples per second), maximumreference picture size, and so on. Limits set by levels can, in somecases, be further restricted through Hypothetical Reference Decoder(HRD) specifications and metadata for HRD buffer management signaled inthe coded video sequence.

In an embodiment, the receiver (331) may receive additional (redundant)data with the encoded video. The additional data may be included as partof the coded video sequence(s). The additional data may be used by thevideo decoder (310) to properly decode the data and/or to moreaccurately reconstruct the original video data. Additional data can bein the form of, for example, temporal, spatial, or signal noise ratio(SNR) enhancement layers, redundant slices, redundant pictures, forwarderror correction codes, and so on.

FIG. 4 shows a block diagram of a video encoder (403) according to anembodiment of the present disclosure. The video encoder (403) isincluded in an electronic device (420). The electronic device (420)includes a transmitter (440) (e.g., transmitting circuitry). The videoencoder (403) can be used in the place of the video encoder (203) in theFIG. 2 example.

The video encoder (403) may receive video samples from a video source(401) (that is not part of the electronic device (420) in the FIG. 4example) that may capture video image(s) to be coded by the videoencoder (403). In another example, the video source (401) is a part ofthe electronic device (420).

The video source (401) may provide the source video sequence to be codedby the video encoder (403) in the form of a digital video sample streamthat can be of any suitable bit depth (for example: 8 bit, 10 bit, 12bit, . . . ), any colorspace (for example, BT.601 Y CrCB, RGB, . . . ),and any suitable sampling structure (for example Y CrCb 4:2:0, Y CrCb4:4:4). In a media serving system, the video source (401) may be astorage device storing previously prepared video. In a videoconferencingsystem, the video source (401) may be a camera that captures local imageinformation as a video sequence. Video data may be provided as aplurality of individual pictures that impart motion when viewed insequence. The pictures themselves may be organized as a spatial array ofpixels, wherein each pixel can comprise one or more samples depending onthe sampling structure, color space, etc. in use. A person skilled inthe art can readily understand the relationship between pixels andsamples. The description below focuses on samples.

According to an embodiment, the video encoder (403) may code andcompress the pictures of the source video sequence into a coded videosequence (443) in real time or under any other time constraints asrequired by the application. Enforcing appropriate coding speed is onefunction of a controller (450). In some embodiments, the controller(450) controls other functional units as described below and isfunctionally coupled to the other functional units. The coupling is notdepicted for clarity. Parameters set by the controller (450) can includerate control related parameters (picture skip, quantizer, lambda valueof rate-distortion optimization techniques, . . . ), picture size, groupof pictures (GOP) layout, maximum motion vector search range, and soforth. The controller (450) can be configured to have other suitablefunctions that pertain to the video encoder (403) optimized for acertain system design.

In some embodiments, the video encoder (403) is configured to operate ina coding loop. As an oversimplified description, in an example, thecoding loop can include a source coder (430) (e.g., responsible forcreating symbols, such as a symbol stream, based on an input picture tobe coded, and a reference picture(s)), and a (local) decoder (433)embedded in the video encoder (403). The decoder (433) reconstructs thesymbols to create the sample data in a similar manner as a (remote)decoder also would create (as any compression between symbols and codedvideo bitstream is lossless in the video compression technologiesconsidered in the disclosed subject matter). The reconstructed samplestream (sample data) is input to the reference picture memory (434). Asthe decoding of a symbol stream leads to bit-exact results independentof decoder location (local or remote), the content in the referencepicture memory (434) is also bit exact between the local encoder andremote encoder. In other words, the prediction part of an encoder “sees”as reference picture samples exactly the same sample values as a decoderwould “see” when using prediction during decoding. This fundamentalprinciple of reference picture synchronicity (and resulting drift, ifsynchronicity cannot be maintained, for example because of channelerrors) is used in some related arts as well.

The operation of the “local” decoder (433) can be the same as of a“remote” decoder, such as the video decoder (310), which has alreadybeen described in detail above in conjunction with FIG. 3 . Brieflyreferring also to FIG. 3 , however, as symbols are available andencoding/decoding of symbols to a coded video sequence by an entropycoder (445) and the parser (320) can be lossless, the entropy decodingparts of the video decoder (310), including the buffer memory (315), andparser (320) may not be fully implemented in the local decoder (433).

An observation that can be made at this point is that any decodertechnology except the parsing/entropy decoding that is present in adecoder also necessarily needs to be present, in substantially identicalfunctional form, in a corresponding encoder. For this reason, thedisclosed subject matter focuses on decoder operation. The descriptionof encoder technologies can be abbreviated as they are the inverse ofthe comprehensively described decoder technologies. Only in certainareas a more detail description is required and provided below.

During operation, in some examples, the source coder (430) may performmotion compensated predictive coding, which codes an input picturepredictively with reference to one or more previously-coded picture fromthe video sequence that were designated as “reference pictures”. In thismanner, the coding engine (432) codes differences between pixel blocksof an input picture and pixel blocks of reference picture(s) that may beselected as prediction reference(s) to the input picture.

The local video decoder (433) may decode coded video data of picturesthat may be designated as reference pictures, based on symbols createdby the source coder (430). Operations of the coding engine (432) mayadvantageously be lossy processes. When the coded video data may bedecoded at a video decoder (not shown in FIG. 4 ), the reconstructedvideo sequence typically may be a replica of the source video sequencewith some errors. The local video decoder (433) replicates decodingprocesses that may be performed by the video decoder on referencepictures and may cause reconstructed reference pictures to be stored inthe reference picture cache (434). In this manner, the video encoder(403) may store copies of reconstructed reference pictures locally thathave common content as the reconstructed reference pictures that will beobtained by a far-end video decoder (absent transmission errors).

The predictor (435) may perform prediction searches for the codingengine (432). That is, for a new picture to be coded, the predictor(435) may search the reference picture memory (434) for sample data (ascandidate reference pixel blocks) or certain metadata such as referencepicture motion vectors, block shapes, and so on, that may serve as anappropriate prediction reference for the new pictures. The predictor(435) may operate on a sample block-by-pixel block basis to findappropriate prediction references. In some cases, as determined bysearch results obtained by the predictor (435), an input picture mayhave prediction references drawn from multiple reference pictures storedin the reference picture memory (434).

The controller (450) may manage coding operations of the source coder(430), including, for example, setting of parameters and subgroupparameters used for encoding the video data.

Output of all aforementioned functional units may be subjected toentropy coding in the entropy coder (445). The entropy coder (445)translates the symbols as generated by the various functional units intoa coded video sequence, by lossless compressing the symbols according totechnologies such as Huffman coding, variable length coding, arithmeticcoding, and so forth.

The transmitter (440) may buffer the coded video sequence(s) as createdby the entropy coder (445) to prepare for transmission via acommunication channel (460), which may be a hardware/software link to astorage device which would store the encoded video data. The transmitter(440) may merge coded video data from the video coder (403) with otherdata to be transmitted, for example, coded audio data and/or ancillarydata streams (sources not shown).

The controller (450) may manage operation of the video encoder (403).During coding, the controller (450) may assign to each coded picture acertain coded picture type, which may affect the coding techniques thatmay be applied to the respective picture. For example, pictures oftenmay be assigned as one of the following picture types:

An Intra Picture (I picture) may be one that may be coded and decodedwithout using any other picture in the sequence as a source ofprediction. Some video codecs allow for different types of intrapictures, including, for example Independent Decoder Refresh (“IDR”)Pictures. A person skilled in the art is aware of those variants of Ipictures and their respective applications and features.

A predictive picture (P picture) may be one that may be coded anddecoded using intra prediction or inter prediction using at most onemotion vector and reference index to predict the sample values of eachblock.

A bi-directionally predictive picture (B Picture) may be one that may becoded and decoded using intra prediction or inter prediction using atmost two motion vectors and reference indices to predict the samplevalues of each block. Similarly, multiple-predictive pictures can usemore than two reference pictures and associated metadata for thereconstruction of a single block.

Source pictures commonly may be subdivided spatially into a plurality ofsample blocks (for example, blocks of 4×4, 8×8, 4×8, or 16×16 sampleseach) and coded on a block-by-block basis. Blocks may be codedpredictively with reference to other (already coded) blocks asdetermined by the coding assignment applied to the blocks' respectivepictures. For example, blocks of I pictures may be codednon-predictively or they may be coded predictively with reference toalready coded blocks of the same picture (spatial prediction or intraprediction). Pixel blocks of P pictures may be coded predictively, viaspatial prediction or via temporal prediction with reference to onepreviously coded reference picture. Blocks of B pictures may be codedpredictively, via spatial prediction or via temporal prediction withreference to one or two previously coded reference pictures.

The video encoder (403) may perform coding operations according to apredetermined video coding technology or standard, such as ITU-T Rec.H.265. In its operation, the video encoder (403) may perform variouscompression operations, including predictive coding operations thatexploit temporal and spatial redundancies in the input video sequence.The coded video data, therefore, may conform to a syntax specified bythe video coding technology or standard being used.

In an embodiment, the transmitter (440) may transmit additional datawith the encoded video. The source coder (430) may include such data aspart of the coded video sequence. Additional data may comprisetemporal/spatial/SNR enhancement layers, other forms of redundant datasuch as redundant pictures and slices, SEI messages, VUI parameter setfragments, and so on.

A video may be captured as a plurality of source pictures (videopictures) in a temporal sequence. Intra-picture prediction (oftenabbreviated to intra prediction) makes use of spatial correlation in agiven picture, and inter-picture prediction makes uses of the (temporalor other) correlation between the pictures. In an example, a specificpicture under encoding/decoding, which is referred to as a currentpicture, is partitioned into blocks. When a block in the current pictureis similar to a reference block in a previously coded and still bufferedreference picture in the video, the block in the current picture can becoded by a vector that is referred to as a motion vector. The motionvector points to the reference block in the reference picture, and canhave a third dimension identifying the reference picture, in casemultiple reference pictures are in use.

In some embodiments, a bi-prediction technique can be used in theinter-picture prediction. According to the bi-prediction technique, tworeference pictures, such as a first reference picture and a secondreference picture that are both prior in decoding order to the currentpicture in the video (but may be in the past and future, respectively,in display order) are used. A block in the current picture can be codedby a first motion vector that points to a first reference block in thefirst reference picture, and a second motion vector that points to asecond reference block in the second reference picture. The block can bepredicted by a combination of the first reference block and the secondreference block.

Further, a merge mode technique can be used in the inter-pictureprediction to improve coding efficiency.

According to some embodiments of the disclosure, predictions, such asinter-picture predictions and intra-picture predictions are performed inthe unit of blocks. For example, according to the HEVC standard, apicture in a sequence of video pictures is partitioned into coding treeunits (CTU) for compression, the CTUs in a picture have the same size,such as 64×64 pixels, 32×32 pixels, or 16×16 pixels. In general, a CTUincludes three coding tree blocks (CTBs), which are one luma CTB and twochroma CTBs. Each CTU can be recursively quadtree split into one ormultiple coding units (CUs). For example, a CTU of 64×64 pixels can besplit into one CU of 64×64 pixels, or 4 CUs of 32×32 pixels, or 16 CUsof 16×16 pixels. In an example, each CU is analyzed to determine aprediction type for the CU, such as an inter prediction type or an intraprediction type. The CU is split into one or more prediction units (PUs)depending on the temporal and/or spatial predictability. Generally, eachPU includes a luma prediction block (PB), and two chroma PBs. In anembodiment, a prediction operation in coding (encoding/decoding) isperformed in the unit of a prediction block. Using a luma predictionblock as an example of a prediction block, the prediction block includesa matrix of values (e.g., luma values) for pixels, such as 8×8 pixels,16×16 pixels, 8×16 pixels, 16×8 pixels, and the like.

FIG. 5 shows a diagram of a video encoder (503) according to anotherembodiment of the disclosure. The video encoder (503) is configured toreceive a processing block (e.g., a prediction block) of sample valueswithin a current video picture in a sequence of video pictures, andencode the processing block into a coded picture that is part of a codedvideo sequence. In an example, the video encoder (503) is used in theplace of the video encoder (203) in the FIG. 2 example.

In an HEVC example, the video encoder (503) receives a matrix of samplevalues for a processing block, such as a prediction block of 8×8samples, and the like. The video encoder (503) determines whether theprocessing block is best coded using intra mode, inter mode, orbi-prediction mode using, for example, rate-distortion optimization.When the processing block is to be coded in intra mode, the videoencoder (503) may use an intra prediction technique to encode theprocessing block into the coded picture; and when the processing blockis to be coded in inter mode or bi-prediction mode, the video encoder(503) may use an inter prediction or bi-prediction technique,respectively, to encode the processing block into the coded picture. Incertain video coding technologies, merge mode can be an inter pictureprediction submode where the motion vector is derived from one or moremotion vector predictors without the benefit of a coded motion vectorcomponent outside the predictors. In certain other video codingtechnologies, a motion vector component applicable to the subject blockmay be present. In an example, the video encoder (503) includes othercomponents, such as a mode decision module (not shown) to determine themode of the processing blocks.

In the FIG. 5 example, the video encoder (503) includes the interencoder (530), an intra encoder (522), a residue calculator (523), aswitch (526), a residue encoder (524), a general controller (521), andan entropy encoder (525) coupled together as shown in FIG. 5 .

The inter encoder (530) is configured to receive the samples of thecurrent block (e.g., a processing block), compare the block to one ormore reference blocks in reference pictures (e.g., blocks in previouspictures and later pictures), generate inter prediction information(e.g., description of redundant information according to inter encodingtechnique, motion vectors, merge mode information), and calculate interprediction results (e.g., predicted block) based on the inter predictioninformation using any suitable technique. In some examples, thereference pictures are decoded reference pictures that are decoded basedon the encoded video information.

The intra encoder (522) is configured to receive the samples of thecurrent block (e.g., a processing block), in some cases compare theblock to blocks already coded in the same picture, generate quantizedcoefficients after transform, and in some cases also intra predictioninformation (e.g., an intra prediction direction information accordingto one or more intra encoding techniques). In an example, the intraencoder (522) also calculates intra prediction results (e.g., predictedblock) based on the intra prediction information and reference blocks inthe same picture.

The general controller (521) is configured to determine general controldata and control other components of the video encoder (503) based onthe general control data. In an example, the general controller (521)determines the mode of the block, and provides a control signal to theswitch (526) based on the mode. For example, when the mode is the intramode, the general controller (521) controls the switch (526) to selectthe intra mode result for use by the residue calculator (523), andcontrols the entropy encoder (525) to select the intra predictioninformation and include the intra prediction information in thebitstream; and when the mode is the inter mode, the general controller(521) controls the switch (526) to select the inter prediction resultfor use by the residue calculator (523), and controls the entropyencoder (525) to select the inter prediction information and include theinter prediction information in the bitstream.

The residue calculator (523) is configured to calculate a difference(residue data) between the received block and prediction resultsselected from the intra encoder (522) or the inter encoder (530). Theresidue encoder (524) is configured to operate based on the residue datato encode the residue data to generate the transform coefficients. In anexample, the residue encoder (524) is configured to convert the residuedata from a spatial domain to a frequency domain, and generate thetransform coefficients. The transform coefficients are then subject toquantization processing to obtain quantized transform coefficients. Invarious embodiments, the video encoder (503) also includes a residuedecoder (528). The residue decoder (528) is configured to performinverse-transform, and generate the decoded residue data. The decodedresidue data can be suitably used by the intra encoder (522) and theinter encoder (530). For example, the inter encoder (530) can generatedecoded blocks based on the decoded residue data and inter predictioninformation, and the intra encoder (522) can generate decoded blocksbased on the decoded residue data and the intra prediction information.The decoded blocks are suitably processed to generate decoded picturesand the decoded pictures can be buffered in a memory circuit (not shown)and used as reference pictures in some examples.

The entropy encoder (525) is configured to format the bitstream toinclude the encoded block. The entropy encoder (525) is configured toinclude various information according to a suitable standard, such asthe HEVC standard. In an example, the entropy encoder (525) isconfigured to include the general control data, the selected predictioninformation (e.g., intra prediction information or inter predictioninformation), the residue information, and other suitable information inthe bitstream. Note that, according to the disclosed subject matter,when coding a block in the merge submode of either inter mode orbi-prediction mode, there is no residue information.

FIG. 6 shows a diagram of a video decoder (610) according to anotherembodiment of the disclosure. The video decoder (610) is configured toreceive coded pictures that are part of a coded video sequence, anddecode the coded pictures to generate reconstructed pictures. In anexample, the video decoder (610) is used in the place of the videodecoder (210) in the FIG. 2 example.

In the FIG. 6 example, the video decoder (610) includes an entropydecoder (671), an inter decoder (680), a residue decoder (673), areconstruction module (674), and an intra decoder (672) coupled togetheras shown in FIG. 6 .

The entropy decoder (671) can be configured to reconstruct, from thecoded picture, certain symbols that represent the syntax elements ofwhich the coded picture is made up. Such symbols can include, forexample, the mode in which a block is coded (such as, for example, intramode, inter mode, bi-predicted mode, the latter two in merge submode oranother submode), prediction information (such as, for example, intraprediction information or inter prediction information) that canidentify certain sample or metadata that is used for prediction by theintra decoder (672) or the inter decoder (680), respectively, residualinformation in the form of, for example, quantized transformcoefficients, and the like. In an example, when the prediction mode isinter or bi-predicted mode, the inter prediction information is providedto the inter decoder (680); and when the prediction type is the intraprediction type, the intra prediction information is provided to theintra decoder (672). The residual information can be subject to inversequantization and is provided to the residue decoder (673).

The inter decoder (680) is configured to receive the inter predictioninformation, and generate inter prediction results based on the interprediction information.

The intra decoder (672) is configured to receive the intra predictioninformation, and generate prediction results based on the intraprediction information.

The residue decoder (673) is configured to perform inverse quantizationto extract de-quantized transform coefficients, and process thede-quantized transform coefficients to convert the residual from thefrequency domain to the spatial domain. The residue decoder (673) mayalso require certain control information (to include the QuantizerParameter (QP)), and that information may be provided by the entropydecoder (671) (data path not depicted as this may be low volume controlinformation only).

The reconstruction module (674) is configured to combine, in the spatialdomain, the residual as output by the residue decoder (673) and theprediction results (as output by the inter or intra prediction modulesas the case may be) to form a reconstructed block, that may be part ofthe reconstructed picture, which in turn may be part of thereconstructed video. It is noted that other suitable operations, such asa deblocking operation and the like, can be performed to improve thevisual quality.

It is noted that the video encoders (203), (403), and (503), and thevideo decoders (210), (310), and (610) can be implemented using anysuitable technique. In an embodiment, the video encoders (203), (403),and (503), and the video decoders (210), (310), and (610) can beimplemented using one or more integrated circuits. In anotherembodiment, the video encoders (203), (403), and (403), and the videodecoders (210), (310), and (610) can be implemented using one or moreprocessors that execute software instructions.

Aspects of the disclosure provide a set of advanced video codingtechnologies. More specifically, a modified implicit transform approachis proposed.

In video coding society, ITU-T VCEG (Q6/16) and ISO/IEC MPEG (JTC 1/SC29/WG 11) published the H.265/HEVC (High Efficiency Video Coding)standard in 2013 (version 1), 2014 (version 2), 2015 (version 3) and2016 (version 4). Since then, the ITU-T and ISO/IEC have been studyingthe potential need for standardization of future video coding technologywith a compression capability that significantly exceeds that of theHEVC standard (including its extensions). In October 2017, the ITU-T andISO/IEC issued the Joint Call for Proposals on Video Compression withCapability beyond HEVC (CfP). By Feb. 15, 2018, total 22 CfP responseson standard dynamic range (SDR), 12 CfP responses on high dynamic range(HDR), and 12 CfP responses on 360 video categories were submitted,respectively. In April 2018, all received CfP responses were evaluatedin the 122 MPEG/10th JVET (Joint Video Exploration Team—Joint VideoExpert Team) meeting. JVET formally launched the standardization ofnext-generation video coding beyond HEVC (i.e., Versatile Video Coding(VVC)), and the current version of VTM (VVC Test Model)(i.e., VTM3).

In HEVC, the primary transforms may be 4-point, 8-point, 16-point and32-point DCT-2, and the transform core matrices may be represented using8-bit integers, i.e., 8-bit transform core. The transform core matricesof smaller DCT-2 are part of larger DCT-2, as shown below.

4 × 4 transform {64, 64, 64, 64} {83, 36, −36, −83} {64, −64, −64, 64}{36, −83, 83, −36} 8 × 8 transform {64, 64, 64, 64, 64, 64, 64, 64} {89,75, 50, 18, −18, −50, −75, −89} {83, 36, −36, −83, −83, −36, 36, 83}{75, −18, −89, −50, 50, 89, 18, −75} {64, −64, −64, 64, 64, −64, −64,64} {50, −89, 18, 75, −75, −18, 89, −50} {36, −83, 83, −36, −36, 83,−83, 36} {18, −50, 75, −89, 89, −75, 50, −18} 16 × 16 transform {64 6464 64 64 64 64 64 64 64 64 64 64 64 64 64} {90 87 80 70 57 43 25 9 −9−25 −43 −57 −70 −80 −87 −90} {89 75 50 18 −18 −50 −75 −89 −89 −75 −50−18 18 50 75 89} {87 57 9 −43 −80 −90 −70 −25 25 70 90 80 43 −9 −57 −87}{83 36 −36 −83 −83 −36 36 83 83 36 −36 −83 −83 −36 36 83} {80 9 −70 −87−25 57 90 43 −43 −90 −57 25 87 70 −9 −80} {75 −18 −89 −50 50 89 18 −75−75 18 89 50 −50 −89 −18 75} {70 −43 −87 9 90 25 −80 −57 57 80 −25 −90−9 87 43 −70} {64 −64 −64 64 64 −64 −64 64 64 −64 −64 64 −64 −64 −64 64}{57 −80 −25 90 −9 87 43 70 −70 −43 87 9 −90 25 80 −57} {50 −89 18 75 −75−18 89 −50 −50 89 −18 −75 75 18 −89 50} {43 −90 57 25 −87 70 9 −80 80 −9−70 87 −25 −57 90 −43} {36 −83 83 −36 −36 83 −83 36 36 −83 83 −36 −36 83−83 36} {25 −70 90 −80 43 9 −57 87 −87 57 −9 −43 80 −90 70 −25} {18 −5074 −89 89 −75 50 −18 −18 50 −75 89 −89 75 −50 18} {9 −25 43 −57 70 −8087 −90 90 −87 80 −70 57 −43 25 −9} 32 × 32 transform {64 64 64 64 64 6464 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 6464 64} {90 90 88 85 82 78 73 67 61 54 46 38 31 22 13 4 −4 −13 −22 −31−38 −46 −54 −61 −67 −73 −78 −82 −85 −88 −90 −90} {90 87 80 70 57 43 25 9−9 −25 −43 −57 −70 −80 −87 −90 −90 −87 −80 −70 −57 −43 −25 −9 9 25 43 5770 80 87 90} {90 82 67 46 22 −4 −31 −54 −73 −85 −90 −88 −78 −61 −38 −1313 38 61 78 88 90 85 73 54 31 4 −22 −46 −67 −82 −90) {89 75 50 18 −18−50 −75 −89 −89 −75 −50 −18 18 50 75 89 89 75 50 18 −18 −50 −75 −89 −89−75 −50 −18 18 50 75 89} {88 67 31 −13 −54 −82 −90 −78 −46 −4 38 73 9085 61 22 −22 −61 −85 −90 −73 −38 4 46 78 90 82 54 13 −31 −67 −88} {87 579 −43 −80 −90 −70 −25 25 70 90 80 43 −9 −57 −87 −87 −57 −9 43 80 90 7025 −25 −70 −90 −80 −43 9 57 87} {85 46 −13 −67 −90 −73 −22 38 82 88 54−4 −61 −90 −78 −31 31 78 90 61 4 −54 −88 −82 −38 22 73 90 67 13 −46 −85}{83 36 −36 −83 −83 −36 36 83 83 36 −36 −83 −83 −36 36 83 83 36 −36 −83−83 −36 36 83 83 36 −36 −83 −83 −36 36 83} {82 22 −54 −90 −61 13 78 8531 −46 −90 −67 4 73 88 38 −38 −88 −73 −4 67 90 46 −31 −85 −78 −13 61 9054 −22 −82} {80 9 −70 −87 −25 57 90 43 −43 −90 −57 25 87 70 −9 −80 −80−9 70 87 25 −57 −90 −43 43 90 57 −25 −87 −70 9 80} {78 −4 −82 −73 13 8567 −22 −88 −61 31 90 54 −38 −90 −46 46 90 38 −54 −90 −31 61 88 22 −67−85 −13 73 82 4 −78} {75 −18 −89 −50 50 89 18 −75 −75 18 89 50 −50 −89−18 75 75 −18 −89 −50 50 89 18 −75 −75 18 89 50 −50 −89 −18 75} {73 −31−90 −22 78 67 −38 −90 −13 82 61 −46 −88 −4 85 54 −54 85 4 88 46 −61 −8213 90 38 −67 −78 22 90 31 −73} {70 −43 −87 9 90 25 −80 −57 57 80 −25 −90−9 87 43 −70 −70 43 87 −9 −90 −25 80 57 −57 −80 25 90 9 −87 −43 70} {67−54 −78 38 85 −22 −90 4 90 13 −88 −31 82 46 −73 −61 61 73 −46 −82 31 88−13 −90 −4 90 22 −85 −38 78 54 −67} {64 −64 −64 64 64 −64 −64 64 64 −64−64 64 64 −64 −64 64 64 −64 −64 64 64 −64 −64 64 64 −64 −64 64 64 −64−64 64} {61 −73 −46 82 31 −88 −13 90 −4 −90 22 85 −38 −78 54 67 −67 −5478 38 −85 −22 90 4 −90 13 88 −31 −82 46 73 −61} {57 −80 −25 90 −9 −87 4370 −70 −43 87 9 −90 25 80 −57 −57 80 25 −90 9 87 −43 −70 70 43 −87 −9 90−25 −80 57} {54 −85 −4 88 −46 −61 82 13 −90 38 67 −78 −22 90 −31 −73 7331 −90 22 78 −67 −38 90 −13 −82 61 46 −88 4 85 −54} {50 −89 18 75 −75−18 89 −50 −50 89 −18 −75 75 18 −89 50 50 −89 18 75 −75 −18 89 −50 −50−89 −18 −75 745 18 −89 50} {46 −90 38 54 −90 31 61 −88 22 67 −85 13 73−82 4 78 −78 −4 82 −73 −13 85 −67 −22 88 −61 −31 90 −54 −38 90 −46} {43−90 57 25 −87 70 9 −80 80 −9 −70 87 −25 −57 90 −43 −43 90 −57 −25 87 −90−9 80 −80 9 70 −87 25 57 −90 43} {38 −88 73 −4 −67 90 −46 −31 85 −78 1361 −90 54 22 −82 82 −22 −54 90 −61 −13 78 −85 31 46 −90 67 4 −73 88 −38}{36 −83 83 −36 −36 83 83 36 36 −83 83 −36 −36 83 −83 36 36 −83 83 −36−36 83 −83 36 36 −83 83 −36 −36 83 −83 36} {31 −78 90 −61 4 54 −88 82−38 −22 73 −90 67 −13 −46 85 −88 46 13 −67 90 −73 22 38 −82 88 −54 −4 61−90 78 −31} {25 −70 90 −80 43 9 −57 87 −87 57 −9 −43 80 −90 70 −25 −2570 −90 80 −43 −9 57 −87 87 −57 9 43 −80 90 −70 25} {22 −61 85 −90 73 −38−4 46 −78 90 −82 54 −13 −31 67 −88 88 −67 31 13 −54 82 −90 78 −46 4 38−73 90 −85 61 −22} {18 −50 75 −89 89 −75 80 −18 −18 50 −75 89 −89 75 −5018 18 −50 75 −89 89 −75 50 −18 −18 50 −75 89 −89 75 15 18} {13 −38 61−78 88 −90 85 −73 54 −31 40 22 −46 67 −82 90 −90 82 −67 46 −22 −4 31 −5473 −85 90 −88 78 −61 38 −13} {9 −25 43 −57 70 −80 87 −90 90 −87 80 −7057 −43 25 −9 −9 25 −43 57 −70 80 −87 90 −90 87 −80 70 −57 43 −25 9} {4−13 22 −31 38 −46 54 −61 67 −73 78 −82 85 −88 90 −90 90 −90 88 −85 82−78 73 −67 61 −54 46 −38 31 −22 13 −4}

The DCT-2 cores show symmetry/anti-symmetry characteristics. Thus, aso-called “partial butterfly” implementation is supported to reduce thenumber of operation counts (multiplications, adds/subs, shifts), andidentical results of matrix multiplication can be obtained using partialbutterfly.

In VVC, two sub-block transforms are provided. A first sub-blocktransform is SVT or SBT. In JVET-J0024, JVET-K0139 and JVET-L0358, aspatially varying transform (SVT) scheme is proposed. With SVT, forinter prediction residuals, there may be only residual block in thecoding block. Since the residual block is smaller than the coding block,the transform size in SVT is smaller than the coding block size. For theregion which is not covered by the residual block or transform, zeroresidual may be assumed.

More specifically, in JVET-L0358, SVT may also be called Sub-blockTransform (SBT). The sub-block types (SVT-H, SVT-V), sizes and positions(Left half, left quarter, right half, right quarter, top half, topquarter, bottom half, bottom quarter) supported in SBT can be shown inFIGS. 7A-7D. FIGS. 7A-7D illustrate the sub-block types (SVT-H, SVT-V),and the positions (Left half, right half, top half, bottom half)supported in SBT respectively. The shaded region labeled by a letter “A”is a residual block with transform, and the other region is assumed tobe a zero residual without transform.

A second sub-block transform is an Intra Sub-Partitions (ISP). The ISPcoding mode divides luma intra-predicted blocks vertically orhorizontally into 2 or 4 sub-partitions depending on the block sizedimensions, as shown in Table 1. FIG. 8 and FIG. 9 show examples of thetwo possibilities. FIG. 8 illustrates an exemplary division of a 4×8block or a 8×4 block. FIG. 9 illustrates an exemplary division of ablock that is not one of a 4×8 block, a 8×4 bock, or a 4×4 block. Allsub-partitions fulfill the condition of having at least 16 samples. Forchroma components, ISP is not applied.

TABLE 1 Number of sub-partitions depending on the block size Block SizeNumber of Sub-Partitions 4 × 4 Not divided 4 × 8 and 8 × 4 2 All othercases 4

In some embodiments, for each of these sub-partitions, a residual signalcan be generated by entropy decoding the coefficients sent by theencoder and then inverse quantizing and inverse transforming thecoefficients. Then, the sub-partition is intra predicted, and finally,the corresponding reconstructed samples are obtained by adding theresidual signal to the prediction signal. Therefore, the reconstructedvalues of each sub-partition can be available to generate the predictionof the next one, which can repeat the process and so on. Allsub-partitions share the same intra mode.

In some embodiments, the ISP algorithm will only be tested with intramodes that are part of the MPM list. For this reason, if a block usesISP, then the MPM flag can be inferred to be one. Besides, if ISP isused for a certain block, then the MPM list can be modified to excludethe DC mode and to prioritize horizontal intra modes for the ISPhorizontal split and vertical intra modes for the vertical one.

In ISP, each sub-partition can be regarded as a sub-TU, since thetransform and reconstruction is performed individually for eachsub-partition.

In current VVC, besides 4-point, 8-point, 16-point and 32-point DCT-2transforms which are same with HEVC, additional 2-point and 64-pointDCT-2 are also included for a primary transform. The 64-point DCT-2 coredefined in VVC can be shown below as a 64×64 matrix:

{  { aa, aa, aa,aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa,aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa,aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa,aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa }  { bf, bg, bh, bi, bj, bk,bi, bm, bn, bo, bp, bq, br, bs, bt, bu, by, bw, bx, by, bz, ca, cb, cc,cd, ce, cf, cg, ch, ci, cj, ck, −ck, −cj, −ci, −ch, −cg, −cf, −ce, −cd,−cc, −cb, −ca, −bz, −by, −bx, −bw, −by, −bu, −bt, −bs, −br, −bq, −bp,−bo, −bn, −bm, −bi, −bk, −bj, −bi, −bh, −bg, −bf }  { ap, aq, ar, as,at, au, ay, aw, ax, ay, az, ba, bb, bc, bd, be, −be, −bd, −bc, −bb, −ba,−az, −ay, −ax, −aw, −ay, −au, −at, −as, −ar, −aq, −ap, −ap, −aq, −ar,−as, −at, −au, −av, −aw, −ax, −ay, −az, −ba, −bb, −bc, −bd, −be, be, bd,bc, bb, ba, az, ay, ax, aw, av, au, at, as, ar, aq, ap }  { bg, bj, bm,bp, bs, bv, by, cb, ce, ch, ck, −ci, −cf, −cc, −bz, −bw, −bt, −bq, −bn,−bk, −bh, −bf, −bi, −bl, −bo, −br, −bu, −bx, −ca, cd, −cg, −cj, cj, cg,cd, ca, bx, bu, br, bo, bl, bi, bf, bh, bk, bn, bq, bt, bw, bz, cc, cf,ci, −ck, −ch, −ce, −cb, −by, −bv, −bs, −bp, −bm, −bj, −bg }  { ah, ai,aj, ak, al, am, an, ao, −ao, −an, −am, −al, −ak, −aj, −ai, −ah, −ah,−ai, −aj, −ak, −al, −am, an, −ao, ao, an, am, al, ak, aj, ai, ah, ah,ai, aj, ak, al, am, an, ao, −ao, −an, −am, −al, −ak, −aj, −ai, −ah, −ah,−ai, −aj, −ak, −al, −am, −an, −ao, ao, an, am, al, ak, aj, ai, ah }  {bh, bm, br, bw, cb, cg, −ck, −cf, −ca, −bv, −bq, −bl, −bg, −bi, −bn,−bs, −bx, −cc, −ch, cj, ce, bz, bu, bp, bk, bf, bj, bo, bt, by, cd, ci,−ci, −cd, −by, −bt, −bo, −bj, −bf, −bk, −bp, −bu, −bz, −ce, −cj, ch, cc,bx, bs, bn, bi, bg, bl, bq, bv, ca, cf, ck, −cg, −cb, −bw, −br, −bm, −bh}  { aq, at, aw, az, bc, −be, −bb, −ay, −av, −as, −ap, −ar, −au, −ax,−ba, −bd, db, ba, ax, au, ar, ap, as, av, ay, bb, be, −bc, −az, −aw,−at, −aq, −aq, −at, −aw, −az, −bc, be, bb, ay, av, as, ap, ar, au, ax,ba, bd, −bd, −ba, −ax, −au, ar, −ap, −as, −av, −ay, −bb, −be, bc, az,aw, at, aq }  { bi, bp, bw, cd, ck, −ce, −bx, −bq, −bj, −bh, −bo, −bv,−cc, −cj, cf, by, br, bk, bg, bn, bu, cb, ci, −cg, −bz, −bs, −bl, −bf,−bm, −bt, −ca, −ch, ch, ca, bt, bm, bf, bl, bs, bz, cg, −ci, −cb, −bu,−bn, −bg, −bk, −br, −by, −cf, cj, cc, bv, bo, bh, bj, bq, bx, ce, −ck,−cd, −bw, −bp, −bp,− bi }  { ad, ae, af, −ag, −af, −ae, −ad, −ad, −ae,−af, −ag, ag, af, ae, ad, ad, ae, af, ag, −ag, −af, −ae, −ad, −ad, −ae,−af, −ag, ag, af, ae, ad, ad, ae, af, ag, −ag, −af, −ae, −ad, −ad, −ae,−af, −ag, ag, af, ae, ad, ad, ae, af, ag, −ag, −af, −ae, −ad, −ad, −ae,−af, −ag, ag, af, ae, ad }  { bj, bs, cb, ck, −cc, −bt, −bk, −bi, −br,−ca, −cj, cd, bu, bl, bh, bq, bz, ci, −ce, −bv, −bm, −bg, −bp, −by, −ch,cf, bw, bn, bf, bo, bx, cg, −cg, −bx, −bo, −bf, −bn, −bw, −cf, ch, by,bp, bg, bm, bv, ce, −ci, −bz, −bq, −bh, −bl, −bu, −cd, cj, ca, br, bi,bk, bt, cc, −ck, −cb, −bs, −bj }  { ar, aw, bb, −bd, −ay, −at, −ap, −au,−az, −be, ba, av, aq, as, ax, bc, −bc, −ax, −as, − aq, −av, −ba, be, az,au, ap, at, ay, bd, −bb, −aw, −ar, −ar, −aw, −bb, bd, ay, at, ap, au,az, be, −ba, −av, −aq, −as, −ax, −bc, bc, ax, as, aq, av, ba, −be, −az,−au, −ap, −at, −ay, −bd, bb, aw, ar }  { bk, bv, cg, −ce, −bt, −bi, −bm,−bx, −ci, cc, br, bg, bo, bz, ck, −ca, −bp, −bf, −bq, −cb, cj, by, bn,bh, bs, cd, −ch, −bw, −bl, −bj, −bu, −cf, cf, bu, bj, bl, bw, ch, −cd,−bs, −bh, −bn, −by, −cj, cb, bq, bf, bp, ca, −ck, −bz, −bo, −bg, −br,−cc, ci, bx, bm, bi, bt, ce, −cg, −bv, −bk, }  { ai, al, ao, −am, −aj,−ah, −ak, −an, an, ak, ah, aj, am, −ao, −al, −ai, −ai, −al, −ao, am, aj,ah, ak, an, −an, −ak, −ah, −aj, −am, ao, al, ao, −am, −aj, −ah, −ak,−an, an, ak, ah, aj, am, −ao, −al, −ai, −ai, −al, −ao, am, aj, ah, ak,an, −an, −ak, −ah, −aj, −am, ao, al, ai }  { bl, by, −ck, −bx, −bk, −bm,−bz, cj, bw, bj, bn, ca, −ci, −bv, −bi, −bo, −cb, ch, bu, bh, bp, cc,−cg, −bt, −bg, −bq, −cd, cf, bs, bf, br, ce, −ce, −br, −bf, −bs, −cf,cd, bq, bg, bt, cg, −cc, −bp, −bh, −bu, −ch, cb, bo, bi, bv, ci, −ca,−bn, −bj, −bw, −cj, bz, bm, bk, bx, ck, −by, −bl }  { as, az, −bd, −aw,−ap, −av, −bc, ba, at, ar, ay, −be, −ax, −aq, −au, −bb, bb, au, aq, ax,be, −ay, −ar, −at, −ba, bc, av, ap, aw, bd, −az, −as, −as, −az, bd, aw,ap, av, bc, −ba, −at, −ar, −ay, be, ax, aq, au, bb, −bb, −au, −aq, −ax,−be, ay, ar, at, ba, −bc, −av, −ap, −aw, −bd, az, as }  { bm, cb, −cf,−bq, −bi, −bx, cj, bu, bf, bt, ci, −by, −bj, −bp, −ce, cc, bn, bl, ca,−cg, −br, −bh, −bw, ck, bv, bg, bs, ch, −bz, −bk, −bo, −cd, cd, bo, bk,bz, −ch, −bs, −bg, −bv, −ck, bw, bh, br, cg, −ca, −bl, −bn, −cc, ce, bp,bj, by, −ci, −bt, −bf, −bu, −cj, bx, bi, bq, cf, −cb, −bm }  { ab, ac,−ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac,−ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac,−ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab, ab, ac,−ac, −ab, −ab, −ac, ac, ab, ab, ac, −ac, −ab, −ab, −ac, ac, ab }  { bn,ce, −ca, −bj, −br, −ci, bw, bf, bv, −cj, −bs, −bi, −bz, cf, bo, bm, cd,−cb, −bk, −bq, −ch, bx, bg, bu, −ck, −bt, −bh, −by, cg, bp, bl, cc, −cc,−bl, −bp, −cg, by, bh, bt, ck, −bu, −bg, −bx, ch, bq, bk, cb, −cd, −bm,−bo, −cf, bz, bi, bs, cj, −bv, −bf, −bw, ci, br, bj, ca, −ce, −bn }  {at, bc, −ay, −ap, −ax, bd, au, as, bb, −az, −aq, −aw, be, av, ar, ba,−ba, −ar, −av, −be, aw, aq, az, −bb, −as, −au, −bd, ax, ap, ay, −bc,−at, −at, −bc, ay, ap, ax, −bd, −au, −as, −bb, az, aq, aw, −be, −av,−ar, −ba, ba, ar, av, be, −aw, −aq, −az, bb, as, au, bd, −ax, −ap, −ay,be, at }  { bo, ch, −bv, −bh, −ca, cc, bj, bt, −cj, −bq, −bm, −cf, bx,bf, by, −ce, −bl, −br, −ck, bs, bk, cd, bz, −bg, −bw, cg, bn, bp, ci,−bu, bi, −cb, cb, bi, bu, −ci, −bp, −bn, −cg, bw, bg, bz, −cd, −bk, −bs,ck, br, bl, ce, −by, −bf, −bx, cf, bm, bq, cj, −bt, −bj, −cc, ca, bh,bv, −ch, bo }  { bo, ch, −bv, −bh, −ca, cc, bj, bt, −cj, −bq, −bm, −cf,bx, bf, by, −ce, −bl, −br, −ck, bs, bk, cd, bz, −bg, −bw, cg, bn, bp,ci, −bu, bi, −cb, cb, bi, bu, −ci, −bp, −bn, −cg, bw, bg, bz, −cd, −bk,−bs, ck, br, bl, ce, −by, −bf, −bx, cf, bm, bq, cj, −bt, −bj, −cc, ca,bh, bv, −ch, bo }  { aj, ao, −ak, −ai, −an, al, ah, am, −am, −ah, −al,an, ai, ak, −ao, −aj, −aj, −ao, ak, ai, an,−al, −ah, −am, am, ah, al,−an, −ai, −ak, ao, aj, aj, ao, −ak, −ai, −an, al, ah, am, −am, −ah, −al,an, ai, ak, −ao, −aj, −aj, −ao, ak, ai, an, −al, −ah, −am, am, ah, al,−an, −ai, −ak, ao, aj }  { bp, ck, −bq, −bo, −cj, br, bn, ci, −bs, −bm,−ch, bt, bl, cg, −bu, −bk, −cf, bv, bj, ce, −bw, −bi, −cd, bx, bh, cc,−by, −bg, −cb, bz, bf, ca, −ca, −bf, −bz, cb, bg, by, −cc, −bh, −bx, cd,bi, bw, −ce, −bj, −bv, cf, bk, bu, −cg, −bl, −bt, ch, bm, bs, −ci, −bn,−br, cj, bo, bq, −ck, −bp }  { au, −be, −at, −av, bd, as, aw, −bc, −ar,−ax, bb, aq, ay, −ba, −ap, −az, az, ap, ba, −ay, −aq, −bb, ax, ar, bc,−aw, −as, −bd, av, at, be, −au, −au,be, at, av, −bd, −as, −aw, bc, ar,ax, −bb, −aq, −ay, ba, ap, az, −az, −ap, −ba, ay, aq, bb, −ax, −ar, −bc,aw, as, bd, −av, −at, −be, au }  { bq, −ci, −bl, −bv, cd, bg, ca, −by,−bi, −cf, bt, bn, ck, −bo, −bs, cg, bj, bx, −cb, −bf, −cc, bw, bk, ch,−br, −bp, cj, bm, bu, −ce, −bh, −bz, bz, bh, ce, −bu, −bm, −cj, bp, br,−ch, −bk, −bw, cc, bf, cb, −bx, −bj, −cg, bs, bo, −ck, −bn, −bt, cf, bi,by, −ca, −bg, −cd, bv, bl, ci, −bq }  { ae, −ag, −ad, −af, af, ad, ag,−ae, −ae, ag, ad, af, −af, −ad, −ag, ae, ae, −ag, −ad, −af, af, ad, ag,−ae, −ae, ag, ad, af, −af, −ad, −ag, ae, ae, −ag, −ad, −af, af, ad, ag,−ae, −ae, ag, ad, af, −af, −ad, −ag, ae, ae, −ag, −ad, −af, af, ad, ag,−ae, −ae, ag, ad, af, −af, −ad, −ag, ae }  { br, −cf, −bg, −cc, bu, bo,−ci, −bj, −bz, bx, bl, ck, −bm, −bw, ca, bi, ch, −bp, −bt, cd, bf, ce,−bs, −bq, cg, bh, cb, −bv, −bn, cj, bk, by, −by, −bk, −cj, bn, bv, −cb,−bh, −cg, bq, bs, −ce, −bf, −cd, bt, bp, −ch, −bi, −ca, bw, bm, −ck,−bl, −bx, bz, bj, ci, −bo, −bu, cc, bg, cf, −br }  { av, −bb, −ap, −bc,au, aw, −ba, −aq, −bd, at, ax, −az, −ar, −be, as, ay, −ay, −as, be, ar,az, −ax, −at, bd, aq, ba, −aw, −au, bc, ap, bb, −av, −av, bb, ap, bc,−au, −aw, ba, aq, bd, −at, −ax, az, ar, be, −as, −ay, ay, as, −be, −ar,−az, ax, at, −bd, −aq, −ba, aw, au, −bc, −ap, −bb, av }  { bs, −cc, −bi,−cj, bl, bz, −bv, −bp, cf, bf, cg, −bo, −bw, by, bm, −ci, −bh, −cd, br,bt, −cb, −bj, −ck, bk, ca, −bu, −bq, ce, bg, ch, −bn, −bx, bx, bn, −ch,−bg, −ce, bq, bu, −ca, −bk, ck, bj, cb, −bt, −br, cd, bh, ci, −bm, −by,bw, bo, −cg, −bf, −cf, bp, bv, −bz, −bl, cj, bi, cc, −bs }  { ak, −am,−ai, ao, ah, an, −aj, −al, al, aj, −an, −ah, −ao, ai, am, −ak, −ak, am,ai, −ao, −ah, −an, aj, al, −al, −aj, an, ah, ao, −ai, −am, ak, ak, −am,−ai, ao, ah, an, −aj, −al, al, aj, −an, −ah, −ao, ai, am, −ak, −ak, am,ai, −ao, −ah, −an, aj, al, −al, −aj, an, ah, ao, −ai, −am, ak }  { bt,−bz, −bn, cf, bh, ck, −bi, −ce, bo, by, −bu, −bs, ca, bm, −cg, −bg, −cj,bj, cd, −bp, −bx, bv, br, −cb, −bl, ch, bf, ci, −bk, −cc, bq, bw, −bw,−bq, cc, bk, −ci, −bf, −ch, bl, cb, −br, −bv, bx, bp, −cd, −bj, cj, bg,cg, −bm, −ca, bs, bu, −by, −bo, ce, bi, −ck, −bh, −cf, bn, bz, −bt }  {bt, −bz, −bn, cf, bh, ck, −bi, −ce, bo, by, −bu, −bs, ca, bm, −cg, −bg,−cj, bj, cd, −bp, −bx, bv, br, −cb, −bl, ch, bf, ci, −bk, −cc, bq, bw,−bw, −bq, cc, bk, −ci, −bf, −ch, bl, cb, −br, −bv, bx, bp, −cd, −bj, cj,bg, cg, −bm, −ca, bs, bu, −by, −bo, ce, bi, −ck, −bh, −cf, bn, bz, −bt } { aw, ay, −au, ba, as, −bc, −aq, be, ap, bd, −ar, −bb, at, az, −av,−ax, ax, av, −az, −at, bb, ar, −bd, −ap, −be, aq, bc, −as, −ba, au, ay,−aw, −aw, ay, au, −ba, −as, be, aq, −be, −ap, −bd, ar, bb, −at, −az, av,ax, −ax, −av, az, at, −bb, −ar, bd, ap, be, −aq, −bc, as, ba, −au, −ay,aw }  { bu, −bw, −bs, by, bq, −ca, −bo, cc, bm, −ce, −bk, cg, bi, −ci,−bg, ck, bf, cj, −bh, −ch, bj, cf, −bl, −cd, bn, cb, −bp, −bz, br, bx,−bt, −bv, bv, bt, −bx, −br, bz, bp, −cb, −bn, cd, bl, −cf, −bj, ch, bh,−cj, −bf, −ck, bg, ci, −bi, −cg, bk, ce, −bm, −cc, bo, ca, −bq, −by, bs,bw, −bu }  { aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa,−aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa,−aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa,−aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa, −aa, −aa, aa, aa,−aa, −aa, aa }  { bv, −bt, −bx, br, bz, −bp, −cb, bn, cd, −bl, −cf, bj,ch, −bh, −cj, bf, −ck, −bg, ci, bi, −cg, −bk, ce, bm, −cc, −bo, ca, bq,−by, −bs, bw, −bu, −bw, bs, by, −bq, −ca, bo, cc, −bm, −ce, bk, cg, −bi,−ci, bg, ck, −bf, cj, bh, −ch, −bj, cf, bl, −cd, −bn, cb, bp, −bz, −br,bx, bt, −bv }  { ax, −av, −az, at, bb, −ar, −bd, ap, −be, −aq, bc, as,−ba, −au, ay, aw, −aw, −ay, au, ba, −as, −bc, aq, be, −ap, bd, ar, −bb,−at, az, av, −ax, −ax, av, az, −at, −bb, ar, bd, −ap, be, aq, −bc, −as,ba, au, −ay, −aw, aw, ay, −au, −ba, as, bc, −aq, −be, ap, −bd, −ar, bb,at, −az, −av, ax }  { bw, −bq, −cc, bk, ci, −bf, ch, bl, −cb, −br, bv,bx, −bp, −cd, bj, cj, −bg, cg, bm, −ca, −bs, bu, by, −bo, −ce, bi, ck,−bh, cf, bn, −bz, −bt, bt, bz, −bn, −cf, bh, −ck, −bi, ce, bo, −by, −bu,bs, ca, −bm, −cg, bg, −cj, −bj, cd, bp, −bx, −bv, br, cb, −bl, −ch, bf,−ci, −bk, cc, bq, −bw }  { al, −aj, −an, ah, −ao, −ai, am, ak, −ak, −am,ai, ao, −ah, an, aj, −al, −al, aj, an, −ah, ao, ai, −am, −ak, ak, am,−ai, −ao, ah, −an, −aj, al, al, −aj, −an, ah, −ao, −ai, am, ak, −ak,−am, ai, ao, −ah, an, aj, −al, −al, aj, an, −ah, ao, ai, −am, −ak, ak,am, −ai, −ao, ah, −an, −aj, al }  { bx, −bn, −ch, bg, −ce, −bq, bu, ca,−bk, −ck, bj, −cb, −bt, br, cd, −bh, ci, bm, −by, −bw, bo, cg, −bf, cf,bp, −bv, −bz, bl, cj, −bi, cc, bs, −bs, −cc, bi, −cj, −bl, bz, bv, −bp,−cf, −cg, −bo, bw, by, −bm, −ci, bh, −cd, −br, bt, cb, −bj, ck, bk, −ca,−bu, bq, ce, −bg, ch, bn, −bx }  { ay, −as, −be, ar, −az, −ax, at, bd,−aq, ba, aw, −au, −bc, ap, −bb, −av, av, bb, −ap, bc, au, −aw, −ba, aq,−bd, −at, ax, az, −ar, be, as, −ay, −ay, as, be, −ar, az, ax, −at, −bd,aq, −ba, −aw, au, bc, −ap, bb, av, −av, −bb, ap, −bc, −au, aw, ba, −aq,bd, at, −ax, −az, ar, −be, −as, ay }  { by, −bk, cj, bn, −bv, −cb, bh,−cg, −bq, bs, ce, −bf, cd, bt, −bp, −ch, bi, −ca, −bw, bm, ck, −bl, bx,bz, −bj, ci, bo, −bu, −cc, bg, −cf, −br, br, cf, −bg, cc, bu, −bo, −ci,bj, −bz, −bx, bl, −ck, −bm, bw, ca, −bi, ch, bp, −bt, −cd, bf, −ce, −bs,bq, cg, −bh, cb, bv, −bn, −cj, bk, −by }  { af, −ad, ag, ae, −ae, −ag,ad, −af, −af, ad, −ag, −ae, ae, ag, −ad, af, af, −ad, ag, ae, −ae, −ag,ad, −af, −af, ad, −ag, −ae, ae, ag, −ad, af, af, −ad, ag, ae, −ae, −ag,ad, −af, −af, ad, −ag, −ae, ae, ag, −ad, af, af, −ad, ag, ae, −ae, −ag,ad, −af, −af, ad, ag, −ae, ae, ag, −ad, af }  { by, −bk, cj, bn, −bv,−cb, bh, −cg, −bq, bs, ce, −bf, cd, bt, −bp, −ch, bi, −ca, −bw, bm, ck,−bl, bx, bz, −bj, ci, bo, −bu, −cc, bg, −cf, −br, br, cf, −bg, cc, bu,−bo, −ci, bj, −bz, −bx, bl, −ck, −bm, bw, ca, −bi, ch, bp, −bt, −cd, bf,−ce, −bs, bq, cg, −bh, cb, bv, −bn, −cj, bk, −by }  { af, −ad, ag, ae,−ae, −ag, ad, −af,− af, ad, −ag, −ae, ae, ag, −ad, af, af, −ad, ag, ae,−ae, −ag, ad, −af, −af, ad, −ag, −ae, ae, ag, −ad, af, af, ad, ag, ae,−ae, −ag, ad, −af, −af, ad, ag, −ae, ae, ag, −ad, af, af, −ad, ag, ae,−ae, −ag, ad,− af, −af, ad, −ag, −ae, ae, ag, −ad, af }  { bz, −bh, ce,bu, −bm, cj, bp, −br, −ch, bk, −bw, −cc, bf, −cb, −bx, bj, −cg, −bs, bo,ck, −bn, bt, cf, −bi, by, ca, −bg, cd, bv, −bl, ci, bq, −bq, −ci, bl,−bv, −cd, bg, −ca, −by, bi, −cf, −bt, bn −ck, −bo, bs, cg, −bj, bx, cb,−bf, cc, bw, −bk, ch, br, −bp, −cj, bm, −bu, −ce, bh, −bz }  { az, −ap,ba, ay, −aq, bb, ax, −ar, bc, aw, −as, bd, av, −at, be, au, −au, −be,at, −av, −bd, as, −aw −bc, ar, −ax, −bb, aq, −ay, −ba, ap, −az, −az, ap,−ba, −ay, aq, −bb, −ax, ar, −bc, −aw, as, −bd, −av, at, −be, −au, au,be, −at, av, bd, −as, aw, bc, −ar, ax, bb, −aq, ay, ba, −ap, az }  { ca,−bf, bz, cb, −bg, by, cc, −bh, bx, cd, −bi, bw, ce, −bj, bv, cf, −bk,bu, cg, −bl, bt, ch, −bm bs, ci, −bn, br, cj, −bo, bq, ck, −bp, bp, −ck,−bq, bo, −cj, −br, ci, −bs, bm, −ch, −bt, bl, −cg, −bu, bk, −cf, −bv,bj, −ce, −bw, bi, −cd, −bx, bh, −cc, by, bg, −cb, −bz, bf, −ca }  { am,−ah, al, an, −ai, ak, ao, −aj, aj, −ao, −ak, ai, −an, −al, ah, −am, −am,ah, −al, −an, ai, −ak, −ao, aj, −aj, ao, ak, −ai, an, al, −ah, am, am,−ah, al, an, −ai, ak, ao, −aj, aj, −ao, −ak, ai, −an, −al, −ah, −am,−am, ah, −al, −an, ai, −ak, −ao, aj, −aj, ao, ak, −ai, an, al, −ah, am } { cb, −bi, bu, ci, −bp, bn, −cg, −bw, bg, −bz, −cd, bk, −bs, −ck, br,−bl, ce, by, −bf, bx, cf, −bm, bq, −cj, −bt, bj, −cc, −ca, bh, −bv, −ch,bo, −bo, ch, bv, −bh, ca, cc, −bj, bt, cj, −bq, bm, −cf, −bx, bf, −by,ce, bl, −br, ck, bs, −bk, cd, bz, −bg, bw, cg, −bn, bp, −ci, −bu, bi,−cb }  { ba, −ar, av, −be, −aw, aq, −az, −bb, as, −au, bd, ax, −ap, ay,bc, −at, at, −bc, −ay, ap, −ax, −bd, au, −as, bb, az, −aq, aw, be, −av,ar, −ba, −ba, ar, −av, be, aw, −aq, az, bb, −as, au, −bd, −ax, ap, −ay,−bc, at, −at, bc, ay, −ap, ax, bd,− au, as, −bb, −az, aq, −aw, −be, av,−ar, ba }  { cc, −bl, bp, −cg, −by, bh, −bt, ck, bu, −bg, bx, ch, −bq,bk, −cb, −cd, bm, −bo, cf, bz, −bi, bs, −cj, −bv, bf, −bw, −ci, br, −bj,ca, ce, −bn, bn, −ce, −ca, bj, −br, ci, bw, −bf, bv, cj, −bs, bi, −bz,−cf, bo, −bm, cd, cb, −bk, bq, −ch, −bx, bg, −bu, ck, bt, −bh, by, cg,−bp, bl, −cc }  { ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac,−ac, ab, −ab, ac, ac, ab, −ab, ac, ac, −ab, ab, −ac, ac, ab, −ab, ac,ac, −ab, ab, −ac, −ac, ab, −ab, ac, ac, −ab, ab, −ac, −ac, ab, −ab, ac } { cd, −bo, bk, −bz, −ch, bs, −bg, bv, −ck, −bw, bh, −br, cg, ca, −bl,bn, −cc, −ce, bp, −bj, by ci, −bt, bf, −bu, cj, bx −bi, bq, −cf, −cb,bm, −bm, cb, cf, −bq, bi, −bx, −cj, bu, −bf, bt, −ci, −by, bj, −bp, ce,cc, −bn, bl, −ca, −cg, br, −bh, bw, ck, −bv, bg, −bs, ch, bz, −bk, bo,−cd }  { bb, −au, aq, −ax be, ay, −ar, at, −ba, −bc, av, −ap, aw, −bd,−az, as, −as, az, bd, −aw, ap, −av, bc, ba, −at, ar, −ay, −be, ax, −aq,au, −bb, −bb, au, −aq, ax, −be, −ay, ar, −at, ba, bc, −av, ap, −aw, bd,az, −as, as, −az, −bd, aw, −ap, av, −bc, ba, at, −ar, ay, be, −ax, aq,−au, bb }  { ce, −br, bf, −bs, cf, cd, −bq, bg, −bt, cg, cc, −bp, bh,−bu, ch, cb, −bo, bi, −bv, ci, ca, −bn, bj, −bw, cj, bz, −bm, bk, −bx,ck, by, −bl, bl, −by, −ck, bx, −bk, bm, −bz, −cj, bw, −bj, bn, −ca, −ci,bv, −bi, bo, −cb, −ch, bu, −bh, bp, −cc, −cg, bt, −bg, bq, −cd, −cf, bs,−bf, br, −ce }  { an, −ak, ah, −aj, am, ao, −al, ai, −ai, al, −ao, −am,aj, −ah, ak, −an, −an, ak, −ah, aj, −am, −ao, al, −ai, ai, −al, ao, am,−aj, ah, −ak, an, an, −ak, ah, −aj, am, ao, −al, ai, −ai, al, −ao, −am,aj, −ah, ak, −an, −an, ak, −ah, aj, −am, −ao, al, −ai, ai, −al, ao, am,−aj, ah, −ak, an }  { cf, −bu, bj, −bl, bw, −ch, −cd, bs, −bh, bn, −by,cj, cb, −bq, bf, −bp, ca, ck, −bz, bo, −bg, br, −cc, −ci, bx, −bm, bi,−bt, ce, cg, −bv, bk, −bk, bv, −cg, −ce, bt, −bi, bm, −bx, ci, cc, −br,bg, −bo, bz, −ck, −ca, bp, −bf, bq, −cb, −cj, by, −bn, bh, −bs, cd, ch,−bw, bl, −bj, bu, −cf }  { bc, −ax, as, −aq, av, −ba, −be, az, −au, ap,−at, ay, −bd, −bb, aw, −ar, ar, −aw, bb, bd, −ay, at, −ap, au, −az, be,ba, −av, aq, −as, ax, −bc, −bc, ax, −as, aq, −av, ba, be, −az, au, −ap,at, −ay, bd, bb, −aw, ar, −ar, aw, −bb, −bd, ay, −at, ap, −au, az, −be,−ba, av, −aq, as, −ax, bc }  { cg, −bx, bo, −bf, bn, bw, cf, ch, −by,bp, −bg, bm, −bv, ce, ci, −bz, bq, −bh, bl, −bu, cd, cj −ca, br, −bi,bk, −bt, cc, ck, −cb, bs, −bj, −bs, cb, −ck, cc, bt, −bk, bi, −br, ca,−cj, −cd, bu, −bl bh, −bq, bz, −ci, −ce, bv, −bm, bg, −bp, by, −ch, −cf,bw, −bn, bf, −bo, bx, −cg }  { ag, −af, ae, −ad, ad, −ae, af, −ag, −ag,af, −ae, ad, −ad, ae, −af, ag, ag, −af, ae, −ad, ad, −ae, af, −ag, −ag,af, −ae, ad, −ad, ae, −af, ag, ag, −af, ae, −ad, ad, −ae, af, −ag, −ag,af, −ae, ad, −ad, ae, −af, ag, ag, −af, ae, −ad, ad, −ae, af, −ag, −ag,af, −ae, ad, −ad, ae, −af, ag }  { ch, −ca, bt, −bm, bf, −bl, bs, −bz,cg, ci, −cb, bu, −bn, bg, −bk, br, −by, cf, −cj, −cc, bv, −bo bh, −bj,bq, −bx, ce, ck, −cd, bw, −bp, bi, −bi, bp, −bw, cd, −ck, −ce, bx, −bq,bj, −bh, bo, −bv, cc, −cj, −cf, by, −br, bk, −bg, bn, −bu, cb, −ci, −cg,bz, −bs, bl, −bf, bm, −bt, ca, −ch }  { bd, −ba, ax, −au, ar, −ap, as,−av, ay, −bb, be, bc, −az, aw, −at, aq, −aq, at, −aw, az, −bc, −be, bb,ay, av, as, ap, ar, au, ax, ba, bd, bd, ba, ax, au, ar, ap, as, av, ay,bb, be, bc, az, −aw, at, −aq, aq, −at, aw,− az, bc, be, −bb, ay, −av,as, −ap, ar, −au, ax, −ba, bd }  { ci, −cd, by, −bt, bo, −bj, bf, −bk,bp, −bu, bz, −ce, cj, ch, −cc, bx, −bs, bn, −bi, bg, −bl, bq, −bv,  bv,ca, −cf, ck, cg, −cb, bw, −br, bm, −bh, bh, −bm, br, −bw, cb, −cg, −ck,cf, −ca, bv, −bq, bl, −bg,  bi, bn, bs, −bx, cc, −ch, −cj, ce, −bz, bu,−bp, bk, −bf, bj, −bo, bt, −by, cd, −ci }  { ck, −cj, ci, −ch, cg, −cf,ce, −cd, cc, cb, ca, −bz, by, −bx, bw, −bv, bu, −bt, bs, −br, bq, −bp,bo, −bn, bm, −bl, bk, −bj, bi, −bh, bg, −bf, bf, −bg, bh, −bi, bj, −bk,bl, −bm, bn, −bo, bp, −bq, br, −bs, bt, −bu, bv, −bw, bx, −by, bz, −ca,cb, −cc, cd, −ce, cf, −cg, ch, −ci, cj, −ck } } where  { aa, ab, ac, ad,ae, af, ag, ah, ai, aj, ak, al, am, an, ao, ap, aq, ar, as, at, au, av,aw, ax, ay, az, ba, bb, bc, bd, be, bf, bg, bh, bi, bj, bk, bl, bm, bn,bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf,cg, ch, ci, cj, ck, } ={64,83,36,89,75,50,18,90,87,80,70,57,43,25,9,90,90,88,85,82,78,73,67,61,54,46,38,31,22,13,4,91,90,90,90,88,87,86,84,83,81,79,77,73,71,69,65,62,59,56,52,48,44,41,37,33,28,24,20,15,11,7,2}

In addition to DCT-2 and 4×4 DST-7 which have been employed in HEVC, anAdaptive Multiple Transform (AMT, or as known as Enhanced MultipleTransform (EMT), or as known as Multiple Transform Selection (MTS))scheme has been used in VVC for residual coding for both inter and intracoded blocks. The MTS uses multiple selected transforms from the DCT/DSTfamilies other than the current transforms in HEVC. The newly introducedtransform matrices are DST-7, DCT-8. Table 2 shows the basis functionsof the selected DST/DCT.

TABLE 2 Transform basis functions of DCT-2, DST-7 and DCT-8 for N-pointinput Transform Type Basis function T_(i)(j), i, j = 0, 1, . . . , N − 1DCT-2${T_{i}(j)} = {\omega_{0} \cdot \sqrt{\frac{2}{N}} \cdot {\cos\left( \frac{\pi \cdot i \cdot \left( {{2j} + 1} \right)}{2N} \right)}}$${{where}\mspace{14mu}\omega_{0}} = \left\{ \begin{matrix}\sqrt{\frac{2}{N}} & {i = 0} \\1 & {i \neq 0}\end{matrix} \right.$ DCT-8${T_{i}(j)} = {\sqrt{\frac{4}{{2N} + 1}} \cdot {\cos\left( \frac{\pi \cdot \left( {{2i} + 1} \right) \cdot \left( {{2j} + 1} \right)}{{4N} + 2} \right)}}$DST-7${T_{i}(j)} = {\sqrt{\frac{4}{{2N} + 1}} \cdot {\sin\left( \frac{\pi \cdot \left( {{2i} + 1} \right) \cdot \left( {j + 1} \right)}{{2N} + 1} \right)}}$

All the primary transform matrices in VVC may be used with 8-bitrepresentation. The AMT applies to the CUs with both width and heightsmaller than or equal to 32, and whether applying AMT or not iscontrolled by a flag called mts_flag. When the mts_flag is equal to 0,only DCT-2 may be applied for coding the residue. When the mts_flag isequal to 1, an index mts_idx is further signalled using 2 bins tospecify the horizontal and vertical transform to be used according toTable 3, where value 1 means using DST-7 and value 2 means using DCT-8.

TABLE 3 Specification of trTypeHor and trTypeVer depending on mts_idx[ x][ y ][ cIdx ] mts_idx[ xTbY ] [ yTbY ][ cIdx ] trTypeHor trTypeVer −1 00   0 1 1   1 2 1   2 1 2   3 2 2

In VVC Draft 4, an implicit MTS may also be applied in case that theabove signaling based MTS (i.e., explicit MTS) is not used. Withimplicit MTS, the transform selection is made according to the blockwidth and height instead of signaling. More specifically, with implicitMTS as proposed in JVET-M0303, DST-7 is selected for the shorter side ofblock and DCT-2 is selected for the longer side of block. The transformcore, which is a matrix composed by the basis vectors, of DST-7 can bealso represented below:

4-point DST-7: {a, b, c, d} {c, c, 0, −c} {d, −a, −c, b} {b, −d, c, −a}where {a, b, c, d} = {29, 55, 74, 84}. 8-point DST-7: {a, b, c, d, e, f,g, h,} {c, f, h, e, b, −a, −d, −g,} {e, g, b, −c, −h, −d, a, f,} {g, c,−d, −f, a, h, b, −e,} {h, −a, −g, b, f, −c, −e, d,} {f, −e, −a, g, −d,−b, h, −c,} {d, −h, e, −a, −c, g, −f, b,} {b, −d, f, −h, g, −e, c, −a,}where {a, b, c, d, e, f, g, h} = {17, 32, 46, 60, 71, 78, 85, 86}.16-point DST-7: {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p,} {c, f,i, l, o, o, l, i, f, c, 0, −c, −f, −i, −l, −o,} {e, j, o, m, h, c, −b,−g, −l, −p, −k, −f, −a, d, i, n,} {g, n, l, e, −b, −i, −p, −j, −c, d, k,o, h, a, −f, −m,} {i, o, f, −c, −l, −l, −c, f, o, i, 0, −i, −o, −f, c,l,} {k, k, 0, −k, −k, 0, k, k, 0, −k, −k, 0, k, k, 0, −k,} {m, g, −f,−n, −a, l, h, −e, −o, −b, k, i, −d, −p, −c, j,} {o, c, −l, −f, i, i, −f,−l, c, o, 0, −o, −c, l, f, −i,} {p, −a, −o, b, n, −c, −m, d, l, −e, −k,f, j, −g, −i, h,} {n, −e, −i, j, d, −o, a, m, −f, −h, k, c, −p, b, l,−g,} {l, −i, −c, o, −f, −f, o, −c, −i, l, 0, −l, i, c, −o, f,} {j, −m,c, g, −p, f, d, −n, i, a, −k, l, −b, −h, o, −e,} {h, −p, i, −a, −g, o,−j, b, f, −n, k, −c, −e, m, −l, d,} {f, −l, o, −i, c, c, −i, o, −l, f,0, −f, l, −o, i, −c,} {d, −h, l, −p, m, −i, e, −a, −c, g, −k, o, −n, j,−f, b,} {b, −d, f, −h, j, −l, n, −p, o, −m, k, −i, g, −e, c, −a,} where{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p} = {9, 17, 25, 33, 41,49, 56, 62, 66, 72, 77, 81, 83, 87, 89, 90}. 32-point DST-7: {a, b, c,d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A,B, C, D, E, F,} {c, f, i, l, o, r, u, x, A, D, F, C, z, w, t, q, n, k,h, e, b, −a, −d, −g, −j, −m, −p, −s, −v, −y, −B, −E,} {e, j, o, t, y, D,D, y, t, o, j, e, 0, −e, −j, −o, −t, −y, −D, −D, −y, −t, −o, −j, −e, 0,e, j, o, t, Y, D,} {g, n, u, B, D, w, p, i, b, −e, −l, −s, −z, −F, −y,−r, −k, −d, c j, q, x, E, A, t, m, f, −a, −h, −o, −v, −C,} {i, r, A, C,t, k, b, −g, −p, −y, −E, −v, −m, −d, e, n, w, F, x, o, f, −c, −l, −u,−D, −z, −q, −h, a, j, s, B,} {k, v, F, u, j, −a, −l, −w, −E, −t, −i, b,m, x, D, s, h, −c, −n, −y, −C, −r, −g, d, o, z, B, q, f, −e, −p, −A,}{m, z, z, m, 0, −m, −z, −z, −m, 0, m, z, z, m, 0, −m, −z, −z, −m, 0, m,z, z, m, 0, −m, −z, −z, −m, 0, m, z,} {o, D, t, e, −j, −y, −y, −j, e, t,D, o, 0, −o, −D, −t, −e, j, y, y, j, −e, −t, −D, −o, 0, o, D, t, e, −j,−y,} {q, E, n, −c, −t, −B, −k, f, w, y, h, −i, −z, −v, −e, l, C, s, b,−o, −F, −p, a, r, D, m, −d, −u, −A, −j, g, x,} {s, A, h, −k, −D, −p, c,v, x, e, −n, −F, −m, f, y, u, b, −q, −C, −j, i, B, r, −a, −t, −z, −g, l,E, o, −d, −w,} {u, w, −b, −s, −y, −d, q, A, f, −o, −C, −h, m, E, j, −k,−F, −l, i, D, n, −g, −B, −p, e, z, r, −c, −x, −t, a, v,} {w, s, −d, −A,−o, h, E, k, −l, −D, −g, p, z, c, −t, −v, a, x, r, −e, −B, −n, i, F, j,−m, −C, −f, q, y, b, −u,} {y, o, −j, −D, −e, t, t, −e, −D, −j, o, y, 0,−y, −o, j, D, e, −t, −t, e, D, j, −o, −y, 0, y, o, −j, −D, −e, t,} {A,k, −p, −v, e, F, f, −u, −q, j, B, a, −z, −l, o, w, −d, −E, −g, t, r, −i,−C, −b, y, m, −n, −x, c, D, h, −s,} {C, g, −v, −n, o, u, −h, −B, a, D,f, −w, −m, p, t, −i, −A, b, E, e, −x, −l, q, s, −j, −z, c, F, d, −y, −k,r,} {E, c, −B, −f, y, i, −v, −l, s, o, −p, −r, m, u, −j, −x, g, A, −d,−D, a, F, b, −C, −e, z, h, −w, −k, t, n, −q,} {F, −a, −E, b, D, −c, −C,d, B, −e, −A, f, z, −g, −y, h, x, −i, −w, j, v, −k, −u, l, t, −m, −s, n,r, −o, −q, p,} {D, −e, −y, j, t, −o, −o, t, j, −y, −e, D, 0, −D, e, y,−j, −t, o, o, −t, −j, y, e, −D, 0, D, −e, −y, j, t, −o,} {B, −i, −s, r,j, −A, −a, C, −h, −t, q, k, −z, −b, D, −g, −u, p, l, −y, −c, E, −f, −v,o, m, −x, −d, F, −e, −w, n,} {z, −m, −m, z, 0, −z, m, m, −z, 0, −z, −m,−m, z, 0, −z, m, m, −z, 0, z, −m, −m, z, 0, −z, m, m, −z, 0, z, −m,} {x,−q, −g, E, −j, −n, A, −c, −u, t, d, −B, m, k, −D, f, r, −w, −a, y, −p,−h, F, −i, −o, z, −b, −v, s, e, −C, l,} {v, −u, −a, w, −t, −b, x, −s,−c, y, −r, −d, z, −q, −e, A, −p, −f, B, −o, −g, C, −n, −h, D, −m, −i, E,−l, −j, F, −k,} {t, −y, e, o, −D, j, j, −D, o, e, −y, t, 0, −t, y, −e,−o, D, −j, −j, D, −o, −e, y, −t, 0, t, −y, e, o, −D, j,} {r, −C, k, g,−y, v, −d, −n, F, −o, −c, u, −z, h, j, −B, s, −a, −q, D, −l, −f, −x, −w,e, m, −E, p, b, −t, A, −i,} {p, −F, q, −a, −o, E, −r, b, n, −D, s, −c,−m, C, −t, d, l, −B, u, −e, −k, A, −v, f, j, −z, w, −g, −i, y, −x, h,}{n, −B, w, −i, −e, s, −F, r, −d, −j, x, −A, m, a, −o, C, −v, h, f, −t,E, −q, c, k, −y, z, −l, −b, p, −D, u, −g,} {l, −x, C, −q, e, g, −s, E,−v, j, b, −n, z, −A, o, −c, −i, u, −F, t, −h, −d, p, −B, y, −m, a, k,−w, D, −r, f,} {j, −t, D, −y, o, −e, −e, o, −y, D, −t, j, 0, −j, t, −D,y, −o, e, e, −o, y, −D, t, −j, 0, j, −t, D, −y, o, −e,} {h, −p, x, −F,y, −q, i, −a, −g, o, −w, E, −z, r, −j, b, f, −n, v, −D, A, −s, k, −c,−e, m, −u, C, −B, t, −l, d,} {f, −l, r, −x, D, −C, w, −q, k, −e, −a, g,−m, s, −y, E, −B, v, −p, j, −d, −b, h, −n, t, −z, F, −A, u, −o, i, −c,}{d, −h, l, −p, t, −x, B, −F, C, −y, u, −q, m, −i, e, −a, −c, g, −k, o,−s, w, −A, E, −D, z, −v, r, −n, j, −f, b,} {b, −d, f, −h, j, −l, n, −p,r, −t, v, −x, z, −B, D, −F, E, −C, A, −y, w, −u, s, −q, o, −m, k, −i, g,−e, c, −a,} where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r,s, t, u, v, w, x, y, z, A, B, C, D, E, F} = {4, 9, 13, 17, 21, 26, 30,34, 38, 42, 45, 50, 53, 56, 60, 63, 66, 68, 72, 74, 77, 78, 80, 82, 84,85, 86, 88, 88, 89, 90, 90}. 4-point DCT-8: {a, b, c, d,} {b, 0, −b,−b,} {c, −b, −d, a,} {d, −b, a, −c,} where {a, b, c, d} = {84, 74, 55,29}. 8-point DCT-8: {a, b, c, d, e, f, g, h,} {b, e, h, −g, −d, −a, −c,−f,} {c, h, −e, −a, −f, g, b, d,} {d, −g, −a, −h, c, e, −f, −b,} {e, −d,−f, c, g, −b, −h, a,} {f, −a, g, e, −b, h, d, −c,} {g, −c, b, −f, −h, d,−a, e,} {h, −f, d, −b, a, −c, e, −g,} where {a, b, c, d, e, f, g, h} ={86, 85, 78, 71, 60, 46, 32, 17}. 16-point DCT-8: {a, b, c, d, e, f, g,h, i, j, k, l, m, n, o, p,} {b, e, h, k, n, 0, −n, −k, −h, −e, −b, −b,−e, −h, −k, −n,} {c, h, m, −p, −k, −f, −a, −e, −j, −o, n, i, d, b, g,l,} {d, k, −p, −i, −b, −f, −m, n, g, a, h, o, −l, −e, −c, −j,} {e, n,−k, −b, −h, 0, h, b, k, −n, −e, −e, −n, k, b, h,} {f, 0, −f, −f, 0, f,f, 0, −f, −f, 0, f, f, 0, −f, −f,} {g, −n, −a, −m, h, f, −o, −b, −l, i,e, −p, −c, −k, j, d,} {h, −k, −e, n, b, 0, −b, −n, e, k, −h, −h, k, e,−n, −b,} {i, −h, −j, g, k, −f, −l, e, m, −d, −n, c, o, −b, −p, a,} {j,−e, −o, a, −n, −f, i, k, −d, −p, b, −m, −g, h, l, −c,} {k, −b, n, h, −e,0, e, −h, −n, b, −k, −k, b, −n, −h, e,} {l, −b, i, o, −e, f, −p, −h, c,−m, −k, a, −j, −n, d, −g,} {m, −e, d, −l, −n, f, −c, k, o, −g, b, −j,−p, h, −a, i,} {n, −h, b, −e, k, 0, −k, e, −b, h, −n, −n, h, −b, e, −k,}{o, −k, g, −c, b, −f, j, −n, −p, l, −h, d, −a, e, −i, m,} {p, −n, l, −j,h, −f, d, −b, a, −c, e, −g, i, −k, m, −o,} where {a, b, c, d, e, f, g,h, i, j, k, l, m, n, o, p} = {90, 89, 87, 83, 81, 77, 72, 66, 62, 56,49, 41, 33, 25, 17, 9}. 32-point DCT-8: {a, b, c, d, e, f, g, h, i, j,k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C, D, E, F,} {b,e, h, k, n, q, t, w, z, C, F, −E, −B, −y, −v, −s, −p, −m, −j, −g, −d,−a, −c, −f, −i, −l, −o, −r, −u, x, −A, −D,} {c, h, m, r, w, B, 0, −B,−w, −r, −m, −h, −c, −c, −h, −m, r, w, −B, 0, B, w, r, m, h, c, c, h, m,r, w, B,} {d, k, r, y, F, −A, −t, −m, −f, −b, −i, −p, −w, −D, C, v, o,h, a, g, n, u, B, −E, −x, −q, −j, −c, −e, −l, −s, −z,} {e, n, w, F, −y,−p, −g, −c, −l, −u, −D, A, r, i, a, j, s, B, −C, −t, −k, −b, −h, −q, −z,E, v, m, d, f, o, x,} {f, q, B, −A, −p, −e, −g, −r, −C, z, o, d, h, s,D, −y, −n, −c, −i, −t, −E, x, m, b, j, u, F, −w, −l, −a −k, −v,} {g, t,0, −t, −g, −g, −t, 0, t, g, g, t, 0, −t, −g, −g, −t, 0, t, g, g, t, 0,−t, −g, −g, −t, 0, t, g, g, t,} {h, w, −B, −m, −c, −r, 0, r, c, m, B,−w, −h, −h, −w, B, m, c, r, 0, −r, −c, −m, −B, w, h, h, w, −B, −m, −c,−r,} {i, z, −w, −f, −l, −C, t, c, o, F, −q, −a, −r, E, n, d, u, −B, −k,−g, −x, y, h, j, A, −v, −e, −m, −D, s, b, p,} {j, C, −r, −b, −u, z, g,m, F, −o, −e, −x, w, d, p, −E, −l, −h, −A, t, a, s, −B, −i, −k, −D, q,c, v, −y, −f, −n,} {k, F, −m, −i, −D, o, g, B, −q, −e, −z, s, c, x, −u,−a, −v, w, b, t, −y, −d, −r, A, f, p, −C, −h, −n, E, j, l,} {l, −E, −h,−p, A, d, t, −w, −a, −x, s, e, B, −o, −i, −F, k, m, −D, −g, −q, z, c, u,−v, −b, −y, r, f, C, −n, −j,} {m, −B, −c, −w, r, h, 0, −h, −r, w, c, B,−m, −m, B, c, w, −r, −h, 0, h, r, −w, −c, −B, m, m, −B, −c, −w, r, h,}{n, −y, −c, −D, i, s, −t, −h, E, d, x, −o, −m, z, b, C, −j, −r, u, g,−F, −e, −w, p, l, −A, −a, −B, k, q, −v, −f,} {o, −v, −h, C, a, D, −g,−w, n, p, −u, −i, B, b, E, −f, −x, m, q, −t, −j, A, c, F, −e, −y, l, r,−s, −k z, d,} {p, −s, −m, v, j, −y, −g, B, d, −E, −a, −F, c, C, −f, −z,i, w, −l, −t, o, q, −r, −n, u, k, −x, −h, A, e, −D, −b,} {q, −p, −r, o,s, −n, −t, m, u, −l, −v, k, w, −j, −x, i, y, −h, −z, g, A, −f, −B, e, C,−d, −D, c, E, −b, −F, a,} {r, −m, −w, h, B, −c, 0, c, −B, −h, w, m, −r,−r, m, w, −h, −B, c, 0, −c, B, h, −w, −m, r, r, −m, −w, h, B, −c,} {s,−j, −B, a, −C, −i, t, r, −k, −A, b, −D, −h, u, q, −l, −z, c, −E, −g, v,p, −m, −y, d, −F, −f, w, o, −n, −x, e,} {t, −g, 0, g, −t, −t, g, 0, −g,t, t, −g, 0, g, −t, −t, g, 0, −g, t, t, −g, 0, g, −t, −t, g, 0, −g, t,t, −g,} {u, −d, B, n, −k, −E, g, −r, −x, a, −y, −q, h, −F, −j, o, A, −c,v, t, −e, C, m, −l, −D, f, −s, −w, b, −z, −p, i,} {v, −a, w, u, −b, x,t, −c, y, s, −d, z, r, −e, A, q, −f, B, p, −g, C, o, −h, D, n, −i, E, m,−j, F, l, −k,} {w, −c, r, B, −h, m, 0, −m, h, −B, −r, c, −w, −w, c, −r,−B, h, −m, 0, m, −h, B, r, −c, w, w, −c, r, B, −h, m,} {x, −f, m, −E,−q, b, −t, −B, j, −i, A, u, −c, p, F, −n, e, −w, −y, g, −l, D, r, −a, s,C, −k, h, −z, −v, d, −o,} {y, −i, h, −x, −z, j, −g, w, A, −k, f, −v, −B,l, −e, u, C, −m, d, −t, −D, n, −c, s, E, −o, b, −r, −F, p, −a, q,} {z,−l, c, −q, E, u, −g, h, −v, −D, p, −b, m, −A, −y, k, −d, r, −F, −t, f,−i, w, C, −o, a, −n, B, x, −j, e, −s,} {A, −o, c, −j, v, F, −t, h, −e,q, −C, −y, m, −a, l, −x, −D, r, −f, g, −s, E, w, −k, b, −n, z, B, −p, d,−i, u,} {B, −r, h, −c, m, −w, 0, w, −m, c, −h, r, −B, −B, r, −h, c, −m,w, 0, −w, m, −c, h, −r, B, B, −r, h, −c, m, −w,} {C, −u, m, −e, d, −l,t, −B, −D, v, −n, f, −c, k, −s, A, E, −w, o, −g, b, −j, r, −z, −F, x,−p, h, −a, i, −q, y,} {D, −x, r, −l, f, −a, g, −m, s, −y, E, C, −w, q,−k, e, −b, h, −n, t, −z, F, B, −v, p, −j, d, −c, i, −o, u, −A,} {E, −A,w, −s, o, −k, g, −c, b, −f, j, −n, r, −v, z, −D, −F, B, −x, t, −p, l,−h, d, −a, e, −i, m, −q, u, −y, C,} {F, −D, B, −z, x, −v, t, −r, p, −n,l, −j, h, −f, d, −b, a, −c, e, −g, i, −k, m, −o, q, −s, u, −w, y, −A, C,−E,} where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t,u, v, w, x, y, z, A, B, C, D, E, F} = {90, 90, 89, 88, 88, 86, 85, 84,82, 80, 78, 77, 74, 72, 68, 66, 63, 60, 56, 53, 50, 45, 42, 38, 34, 30,26, 21, 17, 13, 9, 4}.

In VVC, in some examples, when both the height and width of the codingblock is smaller than or equal to 64, the transform size can be alwaysthe same as the coding block size. When either the height or width ofthe coding block is larger than 64, when doing the transform or intraprediction, the coding block is further split into multiple sub-blocks,where the width and height of each sub-block is smaller than or equal to64, and one transform is performed on each sub-block.

In VVC Draft v5, MTS can be enabled or disabled in SPS with thefollowing syntaxes in Table 4.

TABLE 4 Syntax for enabling MTS in SPS seq_parameter_set_rbsp( ) {Descriptor ... ...  sps_mts_enabled_flag u(1)  if( sps_mts_enabled_flag) {   sps_explicit_mts_intra_enabled_flag u(1)  sps_explicit_mts_inter_enabled_flag u(1)  } ... ...

In VVC Draft v5, for some cases, DST-7 and/or DCT-8 can be used withoutbeing explicitly signaled, i.e., DST-7 and/or DCT-8 can be usedimplicitly based on information that is available for both encoder anddecoder. These cases include:

-   -   (a) Intra Sub-Partitioning (ISP): For ISP mode, the horizontal        transform is selected as DST-7 as long as the block width is        greater than or equal to 4 and less than or equal to 16, and the        vertical transform is selected as DST-7 as long as the block        height is greater than or equal to 4 and less than or equal to        16.    -   (b) Sub-Block Transform (SBT): For SBT mode, for sub-TU located        at the left half (or quarter) and right half (or quarter) of        current CU, the horizontal transform is DCT-8 and DST-7,        respectively. Otherwise, when sub-TU has same width with current        CU, DCT-2 is used. For sub-TU located at the top half (or        quarter) and bottom half (or quarter) of current CU, the        vertical transform is DCT-8 and DST-7, respectively. Otherwise,        when sub-TU has same height with current CU, DCT-2 is used.    -   (c) MTS disabled in SPS: When sps_mts_enabled_flag is signaled        as true, but both sps_explicit_mts_intra_enabled_flag and        sps_explicit_mts_inter_enabled_flag are signaled as false, for        intra prediction residuals, the horizontal transform is selected        as DST-7 as long as the block width is greater than or equal to        4 and less than or equal to 16, and the vertical transform is        selected as DST-7 as long as the block height is greater than or        equal to 4 and less than or equal to 16.

In VVC, a mode-dependent non-separable secondary transform (NSST) can beapplied between the forward core transform and quantization (at theencoder), and between the de-quantization and inverse core transform (atthe decoder). To keep low complexity, NSST is only applied to the lowfrequency coefficients after the primary transform. If both width (W)and height (H) of a transform coefficient block is larger than or equalto 8, then 8×8 non-separable secondary transform can be applied to thetop-left 8×8 region of the transform coefficients block. Otherwise, ifeither W or H of a transform coefficient block is equal to 4, a 4×4non-separable secondary transform can be applied and the 4×4non-separable transform can be performed on the top-left min(8,W)×min(8, H) region of the transform coefficient block. The abovetransform selection rule can be applied for both luma and chromacomponents.

Matrix multiplication implementation of a non-separable transform isdescribed as follows in formula (1) by using a 4×4 input block as anexample. To apply the non-separable transform, the 4×4 input block X

$\begin{matrix}{X = \begin{bmatrix}X_{00} & X_{01} & X_{02} & X_{03} \\X_{10} & X_{11} & X_{12} & X_{13} \\X_{20} & X_{21} & X_{22} & X_{23} \\X_{30} & X_{31} & X_{32} & X_{33}\end{bmatrix}} & (1)\end{matrix}$is represented as a vector

:

=[X ₀₀ X ₀₁ X ₀₂ X ₀₃ X ₁₀ X ₁₁ X ₁₂ X ₁₃ X ₂₀ X ₂₁ X ₂₂ X ₂₃ X ₃₀ X ₃₁X ₃₂ X ₃₃]^(T)    (2)

The non-separable transform is calculated as

=T·

, where

indicates the transform coefficient vector, and T is a 16×16 transformmatrix. The 16×1 coefficient vector

is subsequently re-organized as 4×4 block using the scanning order forthat block (horizontal, vertical or diagonal). The coefficients withsmaller index can be placed with the smaller scanning index in the 4×4coefficient block. In JEM, a Hypercube-Givens Transform (HyGT) withbutterfly implementation is used instead of matrix multiplication toreduce the complexity of non-separable transform.

In one design of NSST, there can be totally 35×3 non-separable secondarytransforms for both 4×4 and 8×8 block size, where 35 is the number oftransform sets specified by the intra prediction mode, denoted as set,and 3 is the number of NSST candidate for each intra prediction mode.The mapping from the intra prediction mode to the transform set isdefined in Table 5. The transform set applied to luma/chroma transformcoefficients is specified by the corresponding luma/chroma intraprediction modes, according to Table 5. For intra prediction modeslarger than 34 (diagonal prediction direction), the transformcoefficient block is transposed before/after the secondary transform atthe encoder/decoder.

For each transform set, the selected non-separable secondary transformcandidate is further specified by the explicitly signalled CU-level NSSTindex. The index may be signalled in a bitstream one time for each intraCU after transform coefficients and truncated unary binarization isused. The truncated value is 2 in case of planar or DC mode, and 3 forangular intra prediction mode. This NSST index may be signalled onlywhen there is more than one non-zero coefficient in a CU. The defaultvalue may be zero when it is not signalled. Zero value of this syntaxelement may indicate that the secondary transform is not applied to thecurrent CU, values 1-3 indicates which secondary transform from the setshould be applied.

In some embodiments, for each transform set, the selected non-separablesecondary transform candidate can be further specified by the explicitlysignalled CU-level NSST index. The index is signalled in a bitstream onetime for each intra CU after transform coefficients and truncated unarybinarization is used. The truncated value is 2 in case of planar or DCmode, and 3 for angular intra prediction mode. This NSST index issignalled only when there is more than one non-zero coefficient in a CU.The default value is zero when it is not signalled. Zero value of thissyntax element indicates secondary transform is not applied to thecurrent CU. Values 1-3 indicate which secondary transform from the setshould be applied.

TABLE 5 Mapping from intra prediction mode to transform set index intromdoe set intro mode set  0  0 34 34  1  1 35 33  2  2 36 32  3  3 37 31 4  4 38 30  5  5 39 29  6  6 40 28  7  7 41 27  8  8 42 26  9  9 43 2510 10 44 24 11 11 45 23 12 12 46 22 13 13 47 21 14 14 48 20 15 15 49 1916 16 50 18 17 17 51 17 18 18 52 16 19 19 53 15 20 20 54 14 21 21 55 1322 22 56 12 23 23 57 11 24 24 58 10 25 25 59  9 26 26 60  8 27 27 61  728 28 62  6 29 29 63  5 30 30 64  4 31 31 65  3 32 32 66  2 33 33 67(LM) Null

A variant of NSST using transform zero-out scheme, namely Reduced SizeTransform (RST), which is also called Low-Frequency Non-SeparableSecondary Transform (LFNST) in VVC Draft 5, has been proposed inJVET-N0193. The JVET-N0193 checks whether the intra prediction mode isPlanar or DC for entropy coding the transform index of NSST. InJVET-N0193, 4 transform sets are applied, and each transform setincludes three RST transform cores. The three RST transform cores can beeither size 16×48 (or 16×64) (applied for transform coefficient blockwith height and width both being greater than or equal to 8) or 16×16(applied for transform coefficient block with either height or widthbeing equal to 4). For notational convenience, the 16×48 (or 16×64)transform is denoted as RST8×8 and the 16×16 one as RST4×4. For RST8×8,the two alternatives using 16×64 transform cores and 16×48 transformcores are shown in FIG. 10 and FIG. 11 , respectively. FIG. 10 shows areduced secondary transform (RST) using 16×64 secondary transform core.FIG. 11 shows a reduced secondary transform (RST) using 16×48 secondarytransform core. The transform using 16×48 transform cores is adopted inVVC Draft 5.

The index indicating the selection of LFNST kernel, i.e., lfnst_idx, issignaled at the end of CU-level syntax, as indicated in Table 6. Table 6provides syntax at CU-level.

TABLE 6 Syntax of signaling an index for selection of LFNST kernelcoding_unit( x0, y0, cbWidth, cbHeight, treeType ) { Descriptor ... ...   numSigCoeff = 0    numZeroOutSigCoeff = 0    transform_tree( x0, y0,cbWidth, cbHeight, treeType )    lfnstWidth = ( treeType = = DUAL_TREE_   CHROMA ) ?      cbWidth / Sub WidthC : cbWidth    lfnstHeight = (treeType = = DUAL_TREE_    CHROMA ) ?      cbHeight / SubHeightC :cbHeight    if( Min( lfnstWidth, lfnstHeight ) >= 4 &&   sp_lfnst_enabled_flag = = 1 &&     CuPredMode [ x0 ] [ y0 ] = = MODEINTRA &&     IntraSubPartitionsSplitType = = ISP_NO_SPLIT &&    !intra_mip_flag [ x0 ] [ y0 ] ) {    if( ( numSigCoeff >( ( treeType= = SINGLE_    TREE ) ? 2 : 1 ) ) &&     numZeroOutSigCoeff = = 0)    lfnst_idx [ x0 ][ y0 ] ae(v)    }   }  } }

In some examples, a Reduced Transform (RT) maps an N dimensional vectorto an R dimensional vector in a different space, where R/N (R<N) is thereduction factor. The RST matrix is an R×N matrix as follows in formula(2):

$\begin{matrix}{T_{RxN} = \begin{bmatrix}t_{11} & t_{12} & t_{13} & \; & t_{1N} \\\; & \; & \; & \cdots & \; \\t_{21} & t_{22} & t_{23} & \; & t_{2N} \\\; & \vdots & \; & \ddots & \vdots \\t_{R\; 1} & t_{R\; 2} & t_{R\; 3} & \cdots & t_{RN}\end{bmatrix}} & (3)\end{matrix}$where the R rows of the transform are R bases of the N dimensionalspace. The inverse transform matrix for RT is the transpose of itsforward transform. FIG. 12A is a schematic view of forward and transformand FIG. 12B is a schematic view of inverse reduced transform.

The RST8×8 with a reduction factor of 4 (¼ size) can be applied. Hence,instead of 64×64, which is a conventional 8×8 non-separable transformmatrix size, a 16×64 direct matrix is used. In other words, the 64×16inverse RST matrix is used at the decoder side to generate core(primary) transform coefficients in 8×8 top-left regions. The forwardRST8×8 uses 16×64 (or 8×64 for 8×8 block) matrices so that the forwardRST8×8 produces non-zero coefficients only in the top-left 4×4 regionwithin the given 8×8 region. In other words, if RST is applied then the8×8 region except the top-left 4×4 region can have only zerocoefficients. For RST4×4, 16×16 (or 8×16 for 4×4 block) direct matrixmultiplication can be applied.

In addition, for RST8×8, to further reduce the transform matrix size,instead of the using the whole top-left 8×8 coefficients as input forcalculating secondary transform, the top-left three 4×4 coefficients areused as the input for calculating secondary transform. FIGS. 13A-13Bshow different alternatives of RST8×8. FIG. 13A shows example 16×64transform matrices and the whole top-left 8×8 coefficients are appliedas input for calculating secondary transform. FIG. 13B shows example16×46 transform matrices and the top-left three 4×4 coefficients areused as the input for calculating secondary transform.

In some embodiments, an inverse RST can be conditionally applied whenthe following two conditions are satisfied: (a) block size is greaterthan or equal to the given threshold (W>=4 && H>=4); (b) transform skipmode flag is equal to zero.

If both width (W) and height (H) of a transform coefficient block isgreater than 4, then the RST8×8 is applied to the top-left 8×8 region ofthe transform coefficient block. Otherwise, the RST4×4 is applied on thetop-left min(8, W)×min(8, H) region of the transform coefficient block.

If the RST index is equal to 0, RST is not applied. Otherwise, if RSTindex is equal to one, RST is applied, of which kernel is chosen withthe RST index.

Furthermore, RST is applied for intra CU in both intra and inter slices,and for both Luma and Chroma. If a dual tree is enabled, RST indices forLuma and Chroma are signaled separately. For inter slice (the dual treeis disabled), a single RST index is signaled and used for both Luma andChroma components. When the ISP mode is selected, RST is disabled, andRST index is not signaled.

In some embodiments, an RST matrix can be chosen from four transformsets, and each of the transform sets consists of two transforms. Whichtransform set is applied is determined from intra prediction mode as thefollowing: (a) if one of three CCLM modes is indicated, transform set 0is selected. (b) Otherwise, transform set selection is performedaccording to Table 7:

TABLE 7 The transform set selection table Tr. set IntraPredMode indexIntraPredMode < 0 1 0 <= IntraPredMode <= 1 0 2 <= IntraPredMode <= 12 113 <= IntraPredMode <= 23 2 24 <= IntraPredMode <= 44 3 45 <=IntraPredMode <= 55 2 56 <= IntraPredMode 1The index (i.e., IntraPredMode) to access Table 7 has a range of [−14,83], which is a transformed mode index used for wide angle intraprediction.

VVC also includes a Matrix-based intra prediction (MIP) mode. Forpredicting the samples of a rectangular block of width W and height H,MIP takes one line of H reconstructed neighbouring boundary samples thatare located at left of the block, and one line of W reconstructedneighbouring boundary samples above the block as input. If thereconstructed samples are unavailable, they are generated as it is donein the conventional intra prediction.

The generation of the prediction signal is based on the following threesteps:

(a) Out of the boundary samples, four samples in the case of W=H=4 andeight samples in all other cases are extracted by averaging.

(b) A matrix vector multiplication, followed by addition of an offset,is carried out with the averaged samples as an input. The result is areduced prediction signal on a subsampled set of samples in the originalblock.

(c) The prediction signal at the remaining positions is generated fromthe prediction signal on the subsampled set by linear interpolationwhich is a single step linear interpolation in each direction.

The matrices and offset vectors needed to generate the prediction signalare taken from three sets S₀, S₁, S₂ of matrices. The set S₀ consists of18 matrices A₀ ^(i), i∈{0, . . . , 17}, and each of the matrices has 16rows, 4 columns and 18 offset vectors b₀ ^(i), i∈{0, . . . , 17}. Eachof the offset vectors b₀ ^(i) has a size 16. Matrices and offset vectorsof the set S₀ are used for blocks of size 4×4. The set S₁ consists of 10matrices A₁ ^(i), i∈{0, . . . , 9}, each of the matrices has 16 rows, 8columns and 10 offset vectors b₁ ^(i), i∈{0, . . . , 9}. Each of theoffset vectors b₁ ^(i) has a size 16. Matrices and offset vectors of theset S₁ are used for blocks of sizes 4×8, 8×4 and 8×8. Finally, the setS₂ consists of 6 matrices A₂ ^(i), i∈{0, . . . , 5}, each of thematrices has 64 rows, 8 columns and 6 offset vectors b₂ ^(i), i∈{0, . .. , 5} of size 64. Matrices and offset vectors of the set S₂ or parts ofthese matrices and offset vectors are used for all other block-shapes.

FIG. 14 is an illustration of an example MIP for 8×8 blocks. As shown inFIG. 14 , given an 8×8 block, MIP takes four averages along each axis ofthe boundary. The resulting eight input samples enter the matrix vectormultiplication. The matrices are taken from the set S₁. This yields 16samples on the odd positions of the prediction block. Thus, a total of(8·16)/(8·8)=2 multiplications per sample are performed. After adding anoffset, these samples are interpolated vertically by using the reducedtop boundary. Horizontal interpolation follows by using the originalleft boundary. The interpolation process does not require anymultiplications in this case.

In terms of signaling of MIP mode, for each Coding Unit (CU) in intramode, a flag indicating whether an MIP mode is applied on thecorresponding Prediction Unit (PU) or not is sent in the bitstream. Ifan MIP mode is applied, the index predmode of the MIP mode is signaledusing an MPM-list including 3 MPMs.

Here, the derivation of the MPMs is performed using the intra-modes ofthe above and the left PU as follows. There are three fixed mappingtables map_angular_to_mip_(idx), idx ∈{0, 1, 2}, and each tableassociate each conventional intra prediction mode predmode_(Angular)with a specific MIP mode, as described in the following formula (4).predmode_(MIP)=map_angular_to_mip[predmode_(Angular)]  (4)where map_angular_to_mip is a fixed look-up table. The index of themapping table is decided based on the width W and height H of PU, and intotal three indices are available, as described below in formula (5)idx(PU)=idx(W,H)∈{0,1,2}  (5)

The formula (5) indicates from which of the three sets the MIPparameters are to be taken.

To generate the MPM list for current block which is coded by MIP mode,an above MIP mode, namely mode_(MIP) ^(above), and a left MIP mode,namely mode_(MIP) ^(left), are firstly derived. The value of mode_(MIP)^(above) is derived as follows:

(a) If the above PU PU_(above) is available, and it belongs to the sameCTU where the current PU resides, and PU_(above) is coded by MIP usingan MIP mode predmode_(MIP) ^(above) and idx(PU)=idx(PU_(above)),mode_(MIP) ^(above)=predmode_(MIP) ^(above)   (6)

(b) If the above PU PU_(above) is available, and it belongs to the sameCTU where the current PU resides, and PU_(above) is coded using aconventional intra prediction mode predmode_(Angular) ^(above),mode_(MIP) ^(above)=map_angular_to_mip[predmode_(Angular) ^(above)]  (7)

(c) Otherwise,mode_(MIP) ^(above)=−1   (8)which means that this mode is unavailable. The value of mode_(MIP)^(left) is derived in the same way of deriving mode_(MIP) ^(above) butwithout checking whether the left PU belongs to the same CTU where thecurrent PU resides.

Finally, given the derived mode_(MIP) ^(above) and mode_(MIP) ^(left)and three pre-defined fixed default MPM lists list_(idx), idx ∈{0, 1,2}, where each of the MPM lists contains three distinct MIP modes, anMPM list is constructed. The MPM list is constructed based on the givendefault list list_(idx(PU)) and mode_(MIP) ^(above) and mode_(MIP)^(left), by substituting −1 by default values as well as removingduplicate MIP modes.

The flags signaling MIP modes can be illustrated Table 8 which is aCU-level syntax table.

TABLE 8 Syntax of flags signaling MIP modes at CU-level coding_unit( x0,y0, cbWidth, cbHeight, treeType ) { Descriptor ... ...    if(sps_mip_enabled_flag &&     ( Abs( Log2( cbWidth) − Log2(cbHeight) ) <=2) &&      cbWidth <= MaxTbSizeY && cbHeight <= MaxTbSizeY )    intra_mip_flag [ x0 ][ y0 ] ae(v)    if( intra_mip_flag [ x0 ][ y0 ]) {      intra_mip_mpm_flag [ x0 ][ y0 ] ae(v)     if(intra_mip_mpm_flag [ x0 ] [ y0 ] )      intra_mip_mpm_idx [ x0 ][ y0 ]ae(v)     else      intra_mip_mpm_remainded [ x0 ][ y0 ] ae(v)    } else{     if( sps_mrl_enabled_flag && ( ( y0 % CtbSizeY ) > 0 ) )     infra_luma_ref idx [ x0 ][ y0 ] ae(v)     if ( sps_isp_enabled_flag&& intra_luma_ref idx[ x0 ] [ y0 ] =     = 0 &&      ( cbWidth <=MaxTbSizeY && cbHeight <= MaxTbSizeY )      &&      ( cbWidth *cbHeight >MinTbSizeY * MinTbSizeY ) )      intra_subpartitions_mode_flag[ x0 ][ y0 ] ae(v)     if( intra_subpartitions_mode_flag [ x0 ] [ y0 ] == 1 &&      cbWidth <= MaxTbSizeY && cbHeight <= MaxTbSizeY )     intra_subpartitions_split_flag[ x0 ][ y0 ] ae(v)     if(intra_luma_ref id [ x0 ] [ y0 ] = = 0 &&     intra_subpartitions_mode_flag[ x0 ] [ y0 ] = = 0)     infra_luma_mpm_flag[ x0 ][ y0 ] ae(v)     if( intra_luma_mpm_flag[x0 ][ y0 ] ) {      if( intra_luma_ref idx[ x0 ] [ y0 ] = = 0)      infra_luma_not_planar_flag[ x0 ][ y0 ] ae(v)      if(intra_luma_not_planar_flag[ x0 ][ y0 ] )       infra_luma_mpm_idx[ x0 ][y0 ] ae(v)     } else      infra_luma_mpm_remainded[ x0 ][ y0 ] ae(v)   }   }  } ... ...

In some embodiments, the MIP modes can be harmonized with the MPM-basedcoding of the conventional intra-prediction modes as follows. The lumaand chroma MPM-list derivation processes for the conventionalintra-prediction modes uses separate fixed tablesmap_mip_to_angular_(idx), idx ∈{0, 1, 2}, which map an MIP-modepredmode_(MIP) to one of the conventional intra-prediction modespredmode_(Angular)=map_mip_to_angular[predmode_(MIP)]  (9)where map_mip_to_angular is a fixed look-up table. For the luma MPM-listderivation, whenever a neighboring luma block is coded by an MIP modepredmode_(MIP), this block is treated as if it was using theconventional intra-prediction mode predmode_(Angular). For the chromaMPM-list derivation, whenever the current luma block uses an MIP-mode,the same mapping is used to translate the MIP-mode to a conventionalintra prediction mode.

Although various methods are provided above, there are severaldisadvantages in the above described methods. For example, currently,when LFNST is applied, sps_mts_enabled_flag is signaled as true, butboth sps_explicit_mts_intra_enabled_flag andsps_explicit_mts_inter_enabled_flag are signaled as false. For smallblock sizes, the primary transform would be selected using the implicittransform scheme as introduced above, which means DST-7 can be alwaysenabled. However, the LFNST kernels may not work very efficiently withDST-7.

In addition, currently, when MIP is applied, sps_mts_enabled_flag issignaled as true, but both sps_explicit_mts_intra_enabled_flag andsps_explicit_mts_inter_enabled_flag are signaled as false. For smallblock sizes, the primary transform would be selected using the implicittransform scheme as introduced above, which means DST-7 can be alwaysenabled. However, the DST-7 may not work very efficiently with MIPmodes.

According to the embodiments of the present disclosure, methods for animproved implicit transformation selection are provided. Further, eachof the methods (or embodiments), encoder, and decoder may be implementedby processing circuitry (e.g., one or more processors or one or moreintegrated circuits). In one example, the one or more processors executea program that is stored in a non-transitory computer-readable medium.In the following disclosures, the term block may be interpreted as aprediction block, a coding block, or a coding unit, i.e., CU.

According to embodiments of the present disclosure, the term NSST mayalso refer to Reduced Secondary Transform (RST), which is an alternativedesign of non-separable secondary transform, e.g., as described inJVET-M0292 or JVET-N0193, it may also refer to Low-FrequencyNon-Separable Secondary Transform (LFNST) adopted in VVC Draft v5.

According to embodiments of the present disclosure, DST-7 may be alsoreplaced by DST-4.

According to embodiments of the present disclosure, an “implicittransform” indicates a transform scheme selecting a group of non-DCT2transforms (such as DST-1, DCT-5, DST-7, DCT-8, DST-4, DCT-4) withoutany transform index signaling. In this regard, a group of non-DCT2transform can be selected using already coded information that isavailable to both encoder and decoder, including but not limited tointra prediction mode (Planar mode, DC mode, Angular modes), block size,block width, block height, block aspect ratio, block area size, intracoding mode (whether MRL, ISP, MIP is used), position of selectedspatial Merge candidates (top Merge candidate, left Merge candidate),inter prediction mode (inter-PDPC mode, CIIP mode etc.).

In the following disclosures, an “explicit transform” indicates atransform scheme selecting one transform from a group of transform typecandidates (such as DCT-2, DST-1, DCT-5, DST-7, DCT-8, DST-4, DCT-4)with an index signaled to indicate which transform type is selected.

In a first embodiment, the disclosed method includes acquiring transformblock signaling information from a coded video bitstream to determinewhether an implicit transform scheme is applied for primary transformtype selection. When the implicit transform scheme is selected, whichmeans a flag of sps_mts_enabled_flag is signaled as true, and both aflag of sps_explicit_mts_intra_enabled_flag and a flag ofsps_explicit_mts_inter_enabled_flag are signaled as false. Moreover, foran W×H block, if a LFNST index (lfnst_idx) is signaled as 0 (i.e.,fault), and if a TSM is not enabled, the primary transform is selectedusing the following algorithm:

(a) Horizontal transform is DST-7 if W>=T1 and W<=T2. Otherwisehorizontal transform is DCT-2. Example values of T1 include 2 pixels, 4pixels, or 8 pixels. Example values of T2 include 4, 8, 16, or 32.

(b) Vertical transform is DST-7 if H>=T1 and H<=T2. Otherwise verticaltransform is DCT-2. Example values of T1 include 2, 4, or 8. Examplevalues of T2 include 4, 8, 16, or 32.

On the contrary, in some embodiments, if LFNST index is not signaled as0 (i.e., LFNST is applied), the primary transform can be selected asfollows:

(a) In an example, DCT-2 is always selected.

(b) In another example, a predefined transform type other than DCT-7 isselected, such as Hadamard transform, DST-1, DCT-5, Compound OrthonormalTransform (COT), Karhunen-Loève Transform (KLT).

The changes of the proposed method in the first embodiment on top of VVCDraft v5 can be shown below, and changes are highlighted in bold.

In an example, inputs to the above disclosed method in the firstembodiment can be:

(a) a luma location (xTbY, yTbY) specifying the top-left sample of thecurrent luma transform block relative to the top-left luma sample of thecurrent picture,

(b) a variable nTbW specifying the width of the current transform block,

(c) a variable nTbH specifying the height of the current transformblock,

(d) a variable cIdx specifying the color component of the current block,and

(e) an (nTbW)×(nTbH) array d[x][y] of scaled transform coefficients withx=0 . . . nTbW−1, y=0 . . . nTbH−1.

Corresponding output of the above method in the first embodiment can bethe (nTbW)×(nTbH) array r[x][y] of residual samples with x=0 . . .nTbW−1, y=0 . . . nTbH−1.

The variable implicitMtsEnabled in the first embodiment may be derivedas follows:

(a) If sps_mts_enabled_flag is equal to 1 and one of the followingconditions is true, implicitMtsEnabled is set equal to 1.

(b) IntraSubPartitionsSplitType is not equal to ISP_NO_SPLIT.

(c) cu_sbt_flag is equal to 1 and Max(nTbW, nTbH) is less than or equalto 32.

(d) sps_explicit_mts_intra_enabled_flag andsps_explicit_mts_inter_enabled_flag are both equal to 0 andCuPredMode[xTbY][yTbY] is equal to MODE_INTRA and lfnst_idx[x0][y0] isequal to 0.

(e) Otherwise, implicitMtsEnabled is set equal to 0.

The variable trTypeHor specifying the horizontal transform kernel andthe variable trTypeVer specifying the vertical transform kernel in thefirst embodiment may be derived as follows:

(a) If cIdx is greater than 0, trTypeHor and trTypeVer are set equal to0.

(b) Otherwise, if implicitMtsEnabled is equal to 1, the followingapplies:

-   -   (i) If IntraSubPartitionsSplitType is not equal to ISP_NO_SPLIT        or both sps_explicit_mts_intra_enabled_flag and        sps_explicit_mts_inter_enabled_flag are equal to 0 and        CuPredMode[xTbY][yTbY] is equal to MODE_INTRA, trTypeHor and        trTypeVer are derived as follows:        trTypeHor=(nTbW>=4&&nTbW<=16)?1:0        trTypeVer=(nTbH>=4&&nTbH<=16)?1:0    -   (ii) Otherwise (cu_sbt_flag is equal to 1), trTypeHor and        trTypeVer are specified in Table 10 below depending on        cu_sbt_horizontal_flag and cu_sbt_pos_flag.    -   (iii) Otherwise, trTypeHor and trTypeVer are specified in Table        9 below depending on tu_mts_idx[xTbY][yTbY].

Tables 9-10 provide specification of of trTypeHor and trTypeVer that areassociated with the method in the first embodiment.

TABLE 9 Specification of trTypeHor and trTypeVer depending ontu_mts_idx[ x ][ y ] tu_mts_idx [ x0 ][ y0 ] 0 1 2 3 4 trTypeHor 0 1 2 12 trTypeVer 0 1 1 2 2

TABLE 10 Specification of trTypeHor and trTypeVer depending oncu_sbt_horizontal_flag and cu_sbt_pos_flag cu_sbt_horizontal_flagcu_sbt_pos_flag trTypeHor trTypeVer 0 0 2 1 0 1 1 1 1 0 1 2 1 1 1 1

In a second embodiment, when an implicit transform scheme is applied forprimary transform type selection (e.g., sps_mts_enabled_flag is signaledas true, but both sps_explicit_mts_intra_enabled_flag andsps_explicit_mts_inter_enabled_flag are signaled as false), for a W×Hblock with MIP flag (intra_mip_flag) being signaled as 0 (i.e., MIP isnot applied), if TSM is not enabled, the primary transform can beselected using the following algorithm:

(a) Horizontal transform is DST-7 if W>=T1 and W<=T2. Otherwisehorizontal transform is DCT-2. Example values of T1 include: 2, 4, or 8.Example values of T2 include 4, 8, 16, or 32.

(b) Vertical transform is DST-7 if H>=T1 and H<=T2. Otherwise verticaltransform is DCT-2. Example values of T1 include 2, 4, or 8. Examplevalues of T2 include 4, 8, 16, or 32.

When MIP flag is not signaled as 0 (i.e., MIP is applied), in anexample, the primary transform uses DCT-2. In another example, theprimary transform uses non DST-7, such as Hadamard transform, DST-1,DCT-5, COT, KLT.

Alternatively, when the MIP flag (intra_mip_flag) is not equal to 0(i.e., MIP is applied), the implicit transform scheme may be stillapplied. However, the threshold T1 and T2 may be different from the onesused for the implicit transform as introduced above. In an example, T1equals to 2, T2 equals to 4, or 8. In another example, T1 equals to 4,T2 equals to 4 or 8. In yet another example, T1 equals to 8, T2 equalsto 8, 16, or 32. T1 can also equal to 16, T2 equals to 16, or 32.

An example of the changes of proposed method in the second embodiment ontop of VVC Draft v5 are shown below, changes are highlighted in bold.

Inputs to the method in the second embodiment can be:

(a) a luma location (xTbY, yTbY) specifying the top-left sample of thecurrent luma transform block relative to the top-left luma sample of thecurrent picture,

-   -   (b) a variable nTbW specifying the width of the current        transform block,    -   (c) a variable nTbH specifying the height of the current        transform block,    -   (d) a variable cIdx specifying the color component of the        current block, and    -   (e) an (nTbW)×(nTbH) array d[x][y] of scaled transform        coefficients with x=0 . . . nTbW−1, y=0 . . . nTbH−1.

Output of this process is the (nTbW)×(nTbH) array r[x][y] of residualsamples with x=0 . . . nTbW−1, y=0 . . . nTbH−1.

The variable implicitMtsEnabled is derived as follows:

(a) If sps_mts_enabled_flag is equal to 1 and one of the followingconditions is true, implicitMtsEnabled is set equal to 1.

(b) IntraSubPartitionsSplitType is not equal to ISP_NO_SPLIT.

(c) cu_sbt_flag is equal to 1 and Max(nTbW, nTbH) is less than or equalto 32.

(d) sps_explicit_mts_intra_enabled_flag andsps_explicit_mts_inter_enabled_flag are both equal to 0 andCuPredMode[xTbY][yTbY] is equal to MODE_INTRA and intra_mip_flag[x0][y0]is equal to 0.

(e) Otherwise, implicitMtsEnabled is set equal to 0.

The variable trTypeHor specifying the horizontal transform kernel andthe variable trTypeVer specifying the vertical transform kernel in thesecond embodiment can be derived as follows:

(a) If cIdx is greater than 0, trTypeHor and trTypeVer are set equal to0.

(b) Otherwise, if implicitMtsEnabled is equal to 1, the followingapplies:

-   -   (i) If IntraSubPartitionsSplitType is not equal to ISP_NO_SPLIT        or both sps_explicit_mts_intra_enabled_flag and        sps_explicit_mts_inter_enabled_flag are equal to 0 and        CuPredMode[xTbY][yTbY] is equal to MODE_INTRA, trTypeHor and        trTypeVer are derived as follows:        trTypeHor=(nTbW>=4&&nTbW<=16)?1:0        trTypeVer=(nTbH>=4&&nTbH<=16)?1:0    -   (ii) Otherwise (cu_sbt_flag is equal to 1), trTypeHor and        trTypeVer are specified in Table 10 depending on        cu_sbt_horizontal_flag and cu_sbt_pos_flag.    -   (iii) Otherwise, trTypeHor and trTypeVer are specified in Table        9 depending on tu_mts_idx[xTbY][yTbY].

In a third embodiment, the first embodiment and the second embodimentcan be combined, and the spec text changes of proposed method on top ofVVC Draft v5 are shown below, changes are highlighted in bold.

Inputs to the method in the third embodiment can be:

(a) a luma location (xTbY, yTbY) specifying the top-left sample of thecurrent luma transform block relative to the top-left luma sample of thecurrent picture,

(b) a variable nTbW specifying the width of the current transform block,

(c) a variable nTbH specifying the height of the current transformblock,

(d) a variable cIdx specifying the color component of the current block,and

(e) an (nTbW)×(nTbH) array d[x][y] of scaled transform coefficients withx=0 . . . nTbW−1, y=0 . . . nTbH−1.

Output of this process is the (nTbW)×(nTbH) array r[x][y] of residualsamples with x=0 . . . nTbW−1, y=0 . . . nTbH−1.

The variable implicitMtsEnabled in the third embodiment can be derivedas follows:

(a) If sps_mts_enabled_flag is equal to 1 and one of the followingconditions is true, implicitMtsEnabled is set equal to 1.

(b) IntraSubPartitionsSplitType is not equal to ISP_NO_SPLIT.

(c) cu_sbt_flag is equal to 1 and Max(nTbW, nTbH) is less than or equalto 32.

(d) sps_explicit_mts_intra_enabled_flag andsps_explicit_mts_inter_enabled_flag are both equal to 0 andCuPredMode[xTbY][yTbY] is equal to MODE_INTRA and lfnst_idx[x0][y0] isequal to 0 and intra_mip_flag[x0][y0] is equal to 0.

(e) Otherwise, implicitMtsEnabled is set equal to 0.

The variable trTypeHor specifying the horizontal transform kernel andthe variable trTypeVer specifying the vertical transform kernel in thethird embodiment are derived as follows:

(a) If cIdx is greater than 0, trTypeHor and trTypeVer are set equal to0.

(b) Otherwise, if implicitMtsEnabled is equal to 1, the followingapplies:

-   -   (i) If IntraSubPartitionsSplitType is not equal to ISP_NO_SPLIT        or both sps_explicit_mts_intra_enabled_flag and        sps_explicit_mts_inter_enabled_flag are equal to 0 and        CuPredMode[xTbY][yTbY] is equal to MODE_INTRA, trTypeHor and        trTypeVer are derived as follows:        trTypeHor=(nTbW>=4&&nTbW<=16)?1:0        trTypeVer=(nTbH>=4&&nTbH<=16)?1:0    -   (ii) Otherwise (cu_sbt_flag is equal to 1), trTypeHor and        trTypeVer are specified in Table 10 depending on        cu_sbt_horizontal_flag and cu_sbt_pos_flag.    -   (iii) Otherwise, trTypeHor and trTypeVer are specified in Table        9 depending on tu_mts_idx[xTbY][yTbY].

In a fourth embodiment of the present disclosure, a combination ofimplicit transform and explicit transform signaling can be applied. Fora horizontal (or vertical) transform, either an implicit transform or anexplicit transform can be used.

In an example, for a W×H block, if W is greater than or equal to T1 andW is less than or equal to T2, then the horizontal transform type isDST-7. Otherwise, if W is greater than T2 and less than or equal to T3,the horizontal transform type can be either DCT-2 or DST-7 and theselection is signaled. Otherwise, if W is greater than T3 or less thanT1, a default transform type, e.g., DCT-2, is applied. Example values ofT1 include 2, 4, or 8. Example values of T2 include 4, 8, 16, or 32.Example values of T3 include 8, 16, 32, or 64. A combined setting of T1,T2 and T3 can be that T1 equals to 4 (or 2), T2 equals to 16 and T3equals to 32 (or 64).

In another example, for a W×H block, if H is greater than or equal to T1and H is less than or equal to T2, then the vertical transform type isDST-7. Otherwise if H is greater than T2 and less than or equal to T3,the vertical transform type can be either DCT-2 or DST-7 and theselection is signaled. Otherwise, if H is greater than T3 or less thanT1, a default transform type, e.g., DCT-2, is applied. Example values ofT1 include 2, 4, or 8. Example values of T2 include 4, 8, 16, or 32.Example values of T3 include 8, 16, 32, or 64. A combined setting of T1,T2 and T3 can be that T1 equals to 4 (or 2), T2 equals to 16 and T3equals to 32 (or 64).

FIG. 15 shows a flow chart outlining a process (1500) according to anembodiment of the disclosure. The process (1500) can be used in thereconstruction of a block coded in intra mode, so to generate aprediction block for the block under reconstruction. In variousembodiments, the process (1500) can be executed by processing circuitry,such as the processing circuitry in the terminal devices (110), (120),(130) and (140), the processing circuitry that performs functions of thevideo encoder (203), the processing circuitry that performs functions ofthe video decoder (210), the processing circuitry that performsfunctions of the video decoder (310), the processing circuitry thatperforms functions of the video encoder (403), and the like. In someembodiments, the process (1500) can be implemented in softwareinstructions, thus when the processing circuitry executes the softwareinstructions, the processing circuitry performs the process (1500). Theprocess starts at (S1501) and proceeds to (S1510).

At (S1510), transform block signaling information is acquired from acoded video bitstream. The transform block signaling information caninclude at least one of a flag of sps_mts_enabled_flag, a flag ofsps_explicit_mts_intra_enabled_flag, or a flag of Transform Skip Mode(TSM), or the like. The transform block signaling information can alsoinclude a LFNST index (lfnst_idx) or a MIP flag (intra_mip_flag). Whenthe flag of sps_mts_enabled_flag is signaled as true, but both the flagof sps_explicit_mts_intra_enabled_flag and the flag ofsps_explicit_mts_inter_enabled_flag are signaled as false, an implicittransform scheme is applied for primary transform type selection.

At (S1520), a determination can be made by the decoder whether thetransform block signaling information indicates the implicit transformscheme, and at least one of a low-frequency non-separable transform(LFNST) and a matrix-based intra predication mode (MIP) is fault. If theimplicit transform scheme is applied, and at least one of alow-frequency non-separable transform (LFNST) and a matrix-based intrapredication mode (MIP) is fault, the process 1500 proceeds to (S1530).

At (S1530), in response to the determination that the transform blocksignaling information indicates the implicit transform scheme, and atleast one of the LFNST and MIP is signaled as fault, a primary transformtype is determined based on a size of a coding block unit (CU). Theprocess 1500 then proceeds to (S1540), where a primary transform isperformed for a transform block that is partitioned from the CU inaccordance with the determined primary transform type.

At (S1520), if the determination is that the implicit transform schemeis applied, but at least one of a low-frequency non-separable transform(LFNST) and a matrix-based intra predication mode (MIP) is true, theprocess 1500 proceeds to (S1550), where in response to thedetermination, DCT-2 or a transform type other than DCT-7 can beselected. The transform type other than DCT-7 can include Hadamardtransform, DST-1, DCT-5, COT, and KLT.

The techniques described above, can be implemented as computer softwareusing computer-readable instructions and physically stored in one ormore computer-readable media. For example, FIG. 16 shows a computersystem (1600) suitable for implementing certain embodiments of thedisclosed subject matter.

The computer software can be coded using any suitable machine code orcomputer language, that may be subject to assembly, compilation,linking, or like mechanisms to create code comprising instructions thatcan be executed directly, or through interpretation, micro-codeexecution, and the like, by one or more computer central processingunits (CPUs), Graphics Processing Units (GPUs), and the like.

The instructions can be executed on various types of computers orcomponents thereof, including, for example, personal computers, tabletcomputers, servers, smartphones, gaming devices, internet of thingsdevices, and the like.

The components shown in FIG. 16 for computer system (1600) are exemplaryin nature and are not intended to suggest any limitation as to the scopeof use or functionality of the computer software implementingembodiments of the present disclosure. Neither should the configurationof components be interpreted as having any dependency or requirementrelating to any one or combination of components illustrated in theexemplary embodiment of a computer system (1600).

Computer system (1600) may include certain human interface inputdevices. Such a human interface input device may be responsive to inputby one or more human users through, for example, tactile input (such as:keystrokes, swipes, data glove movements), audio input (such as: voice,clapping), visual input (such as: gestures), olfactory input (notdepicted). The human interface devices can also be used to capturecertain media not necessarily directly related to conscious input by ahuman, such as audio (such as: speech, music, ambient sound), images(such as: scanned images, photographic images obtain from a still imagecamera), video (such as two-dimensional video, three-dimensional videoincluding stereoscopic video).

Input human interface devices may include one or more of (only one ofeach depicted): keyboard (1601), mouse (1602), trackpad (1603), touchscreen (1610), data-glove (not shown), joystick (1605), microphone(1606), scanner (1607), camera (1608).

Computer system (1600) may also include certain human interface outputdevices. Such human interface output devices may be stimulating thesenses of one or more human users through, for example, tactile output,sound, light, and smell/taste. Such human interface output devices mayinclude tactile output devices (for example tactile feedback by thetouch-screen (1610), data-glove (not shown), or joystick (1605), butthere can also be tactile feedback devices that do not serve as inputdevices), audio output devices (such as: speakers (1609), headphones(not depicted)), visual output devices (such as screens (1610) toinclude CRT screens, LCD screens, plasma screens, OLED screens, eachwith or without touch-screen input capability, each with or withouttactile feedback capability—some of which may be capable to output twodimensional visual output or more than three dimensional output throughmeans such as stereographic output; virtual-reality glasses (notdepicted), holographic displays and smoke tanks (not depicted)), andprinters (not depicted).

Computer system (1600) can also include human accessible storage devicesand their associated media such as optical media including CD/DVD ROM/RW(1620) with CD/DVD or the like media (1621), thumb-drive (1622),removable hard drive or solid state drive (1623), legacy magnetic mediasuch as tape and floppy disc (not depicted), specialized ROM/ASIC/PLDbased devices such as security dongles (not depicted), and the like.

Those skilled in the art should also understand that term “computerreadable media” as used in connection with the presently disclosedsubject matter does not encompass transmission media, carrier waves, orother transitory signals.

Computer system (1600) can also include an interface to one or morecommunication networks. Networks can for example be wireless, wireline,optical. Networks can further be local, wide-area, metropolitan,vehicular and industrial, real-time, delay-tolerant, and so on. Examplesof networks include local area networks such as Ethernet, wireless LANs,cellular networks to include GSM, 3G, 4G, 5G, LTE and the like, TVwireline or wireless wide area digital networks to include cable TV,satellite TV, and terrestrial broadcast TV, vehicular and industrial toinclude CANBus, and so forth. Certain networks commonly require externalnetwork interface adapters that attached to certain general purpose dataports or peripheral buses (1649) (such as, for example USB ports of thecomputer system (1600)); others are commonly integrated into the core ofthe computer system (1600) by attachment to a system bus as describedbelow (for example Ethernet interface into a PC computer system orcellular network interface into a smartphone computer system). Using anyof these networks, computer system (1600) can communicate with otherentities. Such communication can be uni-directional, receive only (forexample, broadcast TV), uni-directional send-only (for example CANbus tocertain CANbus devices), or bi-directional, for example to othercomputer systems using local or wide area digital networks. Certainprotocols and protocol stacks can be used on each of those networks andnetwork interfaces as described above.

Aforementioned human interface devices, human-accessible storagedevices, and network interfaces can be attached to a core (1640) of thecomputer system (1600).

The core (1640) can include one or more Central Processing Units (CPU)(1641), Graphics Processing Units (GPU) (1642), specialized programmableprocessing units in the form of Field Programmable Gate Areas (FPGA)(1643), hardware accelerators for certain tasks (1644), and so forth.These devices, along with Read-only memory (ROM) (1645), Random-accessmemory (1646), internal mass storage such as internal non-useraccessible hard drives, SSDs, and the like (1647), may be connectedthrough a system bus (1648). In some computer systems, the system bus(1648) can be accessible in the form of one or more physical plugs toenable extensions by additional CPUs, GPU, and the like. The peripheraldevices can be attached either directly to the core's system bus (1648),or through a peripheral bus (1649). Architectures for a peripheral businclude PCI, USB, and the like.

CPUs (1641), GPUs (1642), FPGAs (1643), and accelerators (1644) canexecute certain instructions that, in combination, can make up theaforementioned computer code. That computer code can be stored in ROM(1645) or RAM (1646). Transitional data can be also be stored in RAM(1646), whereas permanent data can be stored for example, in theinternal mass storage (1647). Fast storage and retrieve to any of thememory devices can be enabled through the use of cache memory, that canbe closely associated with one or more CPU (1641), GPU (1642), massstorage (1647), ROM (1645), RAM (1646), and the like.

The computer readable media can have computer code thereon forperforming various computer-implemented operations. The media andcomputer code can be those specially designed and constructed for thepurposes of the present disclosure, or they can be of the kind wellknown and available to those having skill in the computer software arts.

As an example and not by way of limitation, the computer system havingarchitecture (1600), and specifically the core (1640) can providefunctionality as a result of processor(s) (including CPUs, GPUs, FPGA,accelerators, and the like) executing software embodied in one or moretangible, computer-readable media. Such computer-readable media can bemedia associated with user-accessible mass storage as introduced above,as well as certain storage of the core (1640) that are of non-transitorynature, such as core-internal mass storage (1647) or ROM (1645). Thesoftware implementing various embodiments of the present disclosure canbe stored in such devices and executed by core (1640). Acomputer-readable medium can include one or more memory devices orchips, according to particular needs. The software can cause the core(1640) and specifically the processors therein (including CPU, GPU,FPGA, and the like) to execute particular processes or particular partsof particular processes described herein, including defining datastructures stored in RAM (1646) and modifying such data structuresaccording to the processes defined by the software. In addition or as analternative, the computer system can provide functionality as a resultof logic hardwired or otherwise embodied in a circuit (for example:accelerator (1644)), which can operate in place of or together withsoftware to execute particular processes or particular parts ofparticular processes described herein. Reference to software canencompass logic, and vice versa, where appropriate. Reference to acomputer-readable media can encompass a circuit (such as an integratedcircuit (IC)) storing software for execution, a circuit embodying logicfor execution, or both, where appropriate. The present disclosureencompasses any suitable combination of hardware and software.

Appendix A: Acronyms

JEM: joint exploration model

VVC: versatile video coding

BMS: benchmark set

MV: Motion Vector

HEVC: High Efficiency Video Coding

SEI: Supplementary Enhancement Information

VUI: Video Usability Information

GOPs: Groups of Pictures

TUs: Transform Units,

PUs: Prediction Units

CTUs: Coding Tree Units

CTBs: Coding Tree Blocks

PBs: Prediction Blocks

HRD: Hypothetical Reference Decoder

SNR: Signal Noise Ratio

CPUs: Central Processing Units

GPUs: Graphics Processing Units

CRT: Cathode Ray Tube

LCD: Liquid-Crystal Display

OLED: Organic Light-Emitting Diode

CD: Compact Disc

DVD: Digital Video Disc

ROM: Read-Only Memory

RAM: Random Access Memory

ASIC: Application-Specific Integrated Circuit

PLD: Programmable Logic Device

LAN: Local Area Network

GSM: Global System for Mobile communications

LTE: Long-Term Evolution

CANBus: Controller Area Network Bus

USB: Universal Serial Bus

PCI: Peripheral Component Interconnect

FPGA: Field Programmable Gate Areas

SSD: solid-state drive

IC: Integrated Circuit

CU: Coding Unit

While this disclosure has described several exemplary embodiments, thereare alterations, permutations, and various substitute equivalents, whichfall within the scope of the disclosure. It will thus be appreciatedthat those skilled in the art will be able to devise numerous systemsand methods which, although not explicitly shown or described herein,embody the principles of the disclosure and are thus within the spiritand scope thereof

What is claimed is:
 1. A method of video encoding for an encoder, themethod comprising: determining whether (i) an implicit transform schemeis enabled, and (ii) at least one of a low-frequency non-separabletransform (LFNST) and a matrix-based intra predication mode (MIP) isinvalid for a coding unit (CU); in response to a determination that theimplicit transform scheme is enabled, and at least one of the LFNST andMIP is invalid, determining a primary transform type based on a size ofthe CU; performing a primary transform for a transform block that ispartitioned from the CU in accordance with the determined primarytransform type; and outputting a coded bitstream that indicates theprimary transform type of the CU.
 2. The method of claim 1, wherein thedetermining the primary transform type comprises: determining whether atransform skip mode is enabled; and in response to a determination thatthe transform skip mode is not enabled, (i) determining a transform typeDST-7 for a horizontal transform for the transform block, responsive toa width of the CU being equal to or greater than T1 and equal to or lessthan T2; (ii) determining a transform type DCT-2 for the horizontaltransform for the transform block, responsive to the width of the CUbeing less than T1 or greater than T2; (iii) determining a transformtype DST-7 for a vertical transform for the transform block responsiveto a height of the CU being equal to or greater than T1 and equal to orless than T2; and (iv) determining a transform type DCT-2 for thevertical transform for the transform block responsive to the height ofthe CU being less than T1 or greater than T2.
 3. The method of claim 2,wherein T1 is equal to one of 2 pixels, 4 pixels, or 8 pixels, and T2 isequal to one of 4 pixels, 8 pixels, 16 pixels, or 32 pixels.
 4. Themethod of claim 1, wherein in response to a determination that theimplicit transform scheme is enabled, and the at least one of the LFNSTor MIP is valid, the method comprises at least one of: (i) determining afirst transform type DCT-2 for the transform block; and (ii) determininga second transform type that is not DCT-7 for the transform block, thesecond transform type including at least one of Hadamard transform,DST-1, DCT-5, compound orthonormal transform (COT), or Karhunen-Loèvetransform.
 5. The method of claim 1, wherein in response to adetermination that the implicit transform scheme is enabled, and the MIPis invalid which indicates the MIP is not applied for the transformblock, the method comprises at least one of: (i) determining a transformtype DST-7 for a horizontal transform for the transform block responsiveto a width of the CU being equal to or greater than T1 and equal to orless than T2; (ii) determining a transform type DCT-2 for the horizontaltransform for the transform block responsive to the width of the CUbeing less than T1 or greater than T2; (iii) determining a transformtype DST-7 for a vertical transform for the transform block responsiveto a height of the CU being equal to or greater than T1 and equal to orless than T2; and (iv) determining a transform type DCT-2 for thevertical transform for the transform block responsive to the height ofthe CU being less than T1 or greater than T2.
 6. The method of claim 5,wherein the T1 and T2 indicate at least one of: T1 is equal to 2 pixels,and T2 is equal to one of 4 pixels or 8 pixels; T1 is equal to 4 pixels,and T2 is equal to one of 4 pixels or 8 pixels; T1 is equal to 8 pixels,and T2 is equal to one of 8 pixels, 16 pixels, or 32 pixels; and T1 isequal to 16 pixels, and T2 is equal to one of 16 pixels or 32 pixels. 7.The method of claim 1, in response to a determination that the implicittransform scheme is enabled, and both the LFNST and the MIP are invalidwhich indicates neither the LFNST nor the MIP is applied for thetransform block, the method comprises at least one of: (i) determining atransform type DST-7 for a horizontal transform for the transform blockresponsive to a width of the CU being equal to or greater than T1 andequal to or less than T2; (ii) determining a transform type DCT-2 forthe horizontal transform for the transform block responsive to the widthof the CU being less than T1 or greater than T2; (iii) determining atransform type DST-7 for a vertical transform for the transform blockresponsive to a height of the CU being equal to or greater than T1 andequal to or less than T2; and (iv) determining a transform type DCT-2for the vertical transform of the transform block responsive to theheight of the CU being less than T1 or greater than T2.
 8. A method ofvideo encoding for an encoder, the method comprising: determining aprimary transform type from a plurality of transform types based on asize of a coding unit (CU); and performing a primary transform for atransform block that is partitioned from the CU in accordance with thedetermined primary transform type, wherein: the primary transform typeis determined as a first primary transform type in response to the sizeof the CU being in a first range, the primary transform type isdetermined to be one of the first primary transform type or a secondprimary transform type in response to the size of the CU being in asecond range, and the primary transform type is determined as the secondprimary transform type in response to the size of the CU being in athird range.
 9. The method of claim 8, wherein the determining comprisesat least one of: (i) determining that the primary transform type isDST-7 for a horizontal transform for the transform block responsive tothe size of the CU being in the first range that indicates a width ofthe CU is equal to or greater than T1 and equal to or less than T2; (ii)determining that the primary transform type is one of DST-7 and DCT-2for the horizontal transform for the transform block, responsive to thesize of the CU being in the second range that indicates the width of theCU is greater than T2 and equal to or less than T3; and (iii)determining that the primary transform type is DCT-2 for the horizontaltransform for the transform block responsive to the size of the CU beingin the third range that indicates the width of the CU is less than T1 orgreater than T3.
 10. The method of claim 9, wherein the determiningcomprises at least one of: (i) determining that the primary transformtype is DST-7 for a vertical transform for the transform blockresponsive to the size of the CU being in the first range that indicatesa height of the CU is equal to or greater than T1 and equal to or lessthan T2; (ii) determining that the primary transform type is one ofDST-7 and DCT-2 for the vertical transform for the transform blockresponsive to the size of the CU being in the second range thatindicates the height of the CU is greater than T2 and equal to or lessthan T3; and (iii) determining that the primary transform type is DCT-2for the vertical transform for the transform block responsive to thesize of the CU being in the third range that indicates the height of theCU is less than T1 or greater than T3.
 11. The method of claim 10,wherein: T1 is equal to one of 2 pixels, 4 pixels, or 8 pixels, T2 isequal to one of 4 pixels, 8 pixels, 16 pixels, or 32 pixels, and T3 isequal to one of 8 pixels, 16 pixels, 32 pixels, or 64 pixels.
 12. Anapparatus for video encoding, comprising: processing circuitryconfigured to: determine whether (i) an implicit transform scheme isenabled, and (ii) at least one of a low-frequency non-separabletransform (LFNST) and a matrix-based intra predication mode (MIP) isinvalid for a coding unit (CU); in response to a determination that theimplicit transform scheme is enabled, and at least one of the LFNST andMIP is invalid, determine a primary transform type based on a size ofthe CU; perform a primary transform for a transform block that ispartitioned from the CU in accordance with the determined primarytransform type; and output a coded bitstream that indicates the primarytransform type of the CU.
 13. The apparatus of claim 12, wherein theprocessing circuitry is configured to: determine whether a transformskip mode is enabled; and in response to a determination that thetransform skip mode is not enabled, (i) determine a transform type DST-7for a horizontal transform for the transform block, responsive to awidth of the CU being equal to or greater than T1 and equal to or lessthan T2; (ii) determine a transform type DCT-2 for the horizontaltransform for the transform block, responsive to the width of the CUbeing less than T1 or greater than T2; (iii) determine a transform typeDST-7 for a vertical transform for the transform block responsive to aheight of the CU being equal to or greater than T1 and equal to or lessthan T2; and (iv) determine a transform type DCT-2 for the verticaltransform for the transform block responsive to the height of the CUbeing less than T1 or greater than T2.
 14. The apparatus of claim 12,wherein in response to a determination that the implicit transformscheme is enabled, and the at least one of the LFNST or MIP is valid,the processing circuitry is configured to perform at least one of: (i)determining a first transform type DCT-2 for the transform block; and(ii) determining a second transform type that is not DCT-7 for thetransform block, the second transform type including at least one ofHadamard transform, DST-1, DCT-5, compound orthonormal transform (COT),or Karhunen-Loève transform.
 15. The apparatus of claim 12, wherein inresponse to a determination that the implicit transform scheme isenabled, and the MIP is invalid which indicates the MIP is not appliedfor the transform block, the processing circuitry is configured toperform at least one of: (i) determining a transform type DST-7 for ahorizontal transform for the transform block responsive to a width ofthe CU being equal to or greater than T1 and equal to or less than T2;(ii) determining a transform type DCT-2 for the horizontal transform forthe transform block responsive to the width of the CU being less than T1or greater than T2; (iii) determining a transform type DST-7 for avertical transform for the transform block responsive to a height of theCU being equal to or greater than T1 and equal to or less than T2; and(iv) determining a transform type DCT-2 for the vertical transform forthe transform block responsive to the height of the CU being less thanT1 or greater than T2.
 16. The apparatus of claim 15, wherein the T1 andT2 indicate at least one of: T1 is equal to 2 pixels, and T2 is equal toone of 4 pixels or 8 pixels; T1 is equal to 4 pixels, and T2 is equal toone of 4 pixels or 8 pixels; T1 is equal to 8 pixels, and T2 is equal toone of 8 pixels, 16 pixels, or 32 pixels; and T1 is equal to 16 pixels,and T2 is equal to one of 16 pixels or 32 pixels.
 17. The apparatus ofclaim 12, in response to a determination that the implicit transformscheme is enabled, and both the LFNST and the MIP are invalid whichindicates neither the LFNST nor the MIP is applied for the transformblock, the processing circuitry is configured to perform at least oneof: (i) determining a transform type DST-7 for a horizontal transformfor the transform block responsive to a width of the CU being equal toor greater than T1 and equal to or less than T2; (ii) determining atransform type DCT-2 for the horizontal transform for the transformblock responsive to the width of the CU being less than T1 or greaterthan T2; (iii) determining a transform type DST-7 for a verticaltransform for the transform block responsive to a height of the CU beingequal to or greater than T1 and equal to or less than T2; and (iv)determining a transform type DCT-2 for the vertical transform of thetransform block responsive to the height of the CU being less than T1 orgreater than T2.
 18. An apparatus for video encoding, comprising:processing circuitry configured to: determine a primary transform typefrom a plurality of transform types based on a size of a coding unit(CU); and perform a primary transform for a transform block that ispartitioned from the CU in accordance with the determined primarytransform type, wherein: the primary transform type is determined as afirst primary transform type in response to the size of the CU being ina first range, the primary transform type is determined to be one of thefirst primary transform type or a second primary transform type inresponse to the size of the CU being in a second range, and the primarytransform type is determined as the second primary transform type inresponse to the size of the CU being in a third range.
 19. The apparatusof claim 18, wherein the processing circuitry is further configured toperform at least one of: (i) determining that the primary transform typeis DST-7 for a horizontal transform for the transform block responsiveto the size of the CU being in the first range that indicates a width ofthe CU is equal to or greater than T1 and equal to or less than T2; (ii)determining that the primary transform type is one DST-7 and DCT-2 forthe horizontal transform for the transform block, responsive to the sizeof the CU being in the second range that indicates the width of the CUis greater than T2 and equal to or less than T3; and (iii) determiningthat the primary transform type is DCT-2 for the horizontal transformfor the transform block responsive to the size of the CU being in thethird range that indicates the width of the CU is less than T1 orgreater than T3.
 20. The apparatus of claim 19, wherein the processingcircuitry is further configured to perform at least one of: (i)determining that the primary transform type is DST-7 for a verticaltransform for the transform block responsive to the size of the CU beingin the first range that indicates a height of the CU is equal to orgreater than T1 and equal to or less than T2; (ii) determining that theprimary transform type is one of DST-7 and DCT-2 for the verticaltransform for the transform block responsive to the size of the CU beingin the second range that indicates the height of the CU is greater thanT2 and equal to or less than T3; and (iii) determining that the primarytransform type is DCT-2 for the vertical transform for the transformblock responsive to the size of the CU being in the third range thatindicates the height of the CU is less than T1 or greater than T3.